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Single particle level microscopy of immobilized FAPbBr3 nanocrystals (NCs) has elucidated the involvement of different processes in their photoluminescence (PL) intermittency. Four different blinking patterns are observed in the data from more than 100 NCs. The dependence of PL decays on PL intensities brought out in fluorescence lifetime intensity distribution (FLID) plots is rationalized by the interplay of exciton- and trion-mediated recombinations along with hot carrier (HC) trapping. The high intensity-long lifetime component is attributed to neutral exciton recombination, the low intensity-short lifetime component is attributed to trion assisted recombination, and the low intensity-long lifetime component is attributed to hot carrier recombination. Change-point analysis (CPA) of the PL blinking data reveals the involvement of multiple intermediate states. Truncated power law distribution is found to be more appropriate than power law and lognormal distribution for on and off events. Probability distributions of PL trajectories of single NCs are obtained for two different excitation fluences and wavelengths (λex = 400, 440 nm). Trapping rate (kT) prevails at higher power densities for both excitation wavelengths. From a careful analysis of the FLID and probability distributions, it is concluded that there is competition between the HC and trion assisted blinking pathways and that the contribution of these mechanisms varies with excitation wavelength as well as fluence. [ABSTRACT FROM AUTHOR]

The simulation is often required to assess a new model, identify problems with an existing design, and test a system under conditions that are hard to reproduce in an actual system. In this article, necessary simulations have been carried out on superparamagnetic nanoparticles considering a wide range of particle sizes and distribution widths purposefully to obtain the underlying magnetic features which cannot be envisioned easily by experimental studies. The present study demonstrates that the particle sizes and distribution widths of nanoparticle assembly have significant effect on controlling its ZFC/FC magnetization and isothermal M-H curves. The log-normal distribution function helps us to simulate the magnetic features in a reasonable fashion for distributed nanoparticles. The algorithm used for computer simulation of the present work is quite efficient as far as time is concerned. [ABSTRACT FROM AUTHOR]

It is shown here that if the PDF (Probability Distribution Function) of wind speed is a Rayleigh distribution with parameter $s$ s , then the PDF of wind power is a Weibull distribution with parameters $a = \sqrt 2 \rho s^3\comma \; \; b = \displaystyle{2 \over {3\; }}$ a = 2 ρ s 3 , b = 2 3 , where $\rho$ ρ is the air density; if the wind speed PDF is a Weibull distribution with parameters $a\comma \; b$ a , b , then the wind power PDF is also a Weibull distribution with parameters $\; \displaystyle{{a^3\rho } \over 2}\comma \; \displaystyle{b \over 3}$ a 3 ρ 2 , b 3 ; if the PDF of wind speed is a log-normal distribution with parameters $\mu \comma \; \sigma$ μ , σ , then the PDF of wind power is also a log-normal distribution with parameters $\ln \displaystyle{\rho \over 2} + 3\mu \comma \; 3\sigma$ ln ρ 2 + 3 μ , 3 σ . The derived relationships allow us to quickly estimate parameters that indicate the wind power potential of the considered site, and the amount of wind energy generated by the turbine. [ABSTRACT FROM AUTHOR]

The durability of carbonated recycled aggregate concrete (C-RAC) beams is still unclear at present. In this paper, the characteristics of corrosion-induced cracks and the steel corrosion depth of C-RAC beams were investigated through the accelerated corrosion test. The results showed that when accelerating corrosion to the 40th day, compared to the non-carbonated recycled aggregate concrete (NC-RAC) beam, the corrosion-induced cracking area of the C-RAC beam with a 100% carbonated recycled coarse aggregate (C-RCA) replacement ratio decreased by 40.00%, while the total length of the corrosion-induced cracks (CCs) increased by 51.82%. The type of probability distribution for the width of the CCs on the tension side of the C-RAC beams was a lognormal distribution. Compared with the NC-RAC beam, the mean value of the width of the CCs of the C-RAC beam with a 100% C-RCA replacement ratio decreased by 66.67%, the crack width distribution was more concentrated, and the quartiles and median were all reduced. With an increase in the C-RCA replacement ratio, the fractal dimension and the scale coefficient of CCs on the tension side of the beams showed an approximate trend of first increasing and then decreasing. The distribution of the corrosion depth of longitudinal tensile steel bars in the C-RAC beams was a mainly normal distribution. When the C-RCA replacement ratio increased from 30% to 100%, the mean value of the corrosion depth of the longitudinal tensile steel bars decreased by 33.46%, and the trend of changes in the quartiles and medians was basically the same as the trend of changes in the mean value. The research results can provide some reference for promoting the engineering application of C-RAC beams. [ABSTRACT FROM AUTHOR]

Thanks to the performance improvement introduced by micro sized functional fillers, application of epoxy composites for electrical insulation purposes has become popular. This paper investigates the dielectric properties of epoxy micro-composites filled with alumina (Al2O3). In particular, measurements of relative permittivity, dissipation factor, and electrical breakdown are performed, and a comprehensive statistical analysis on dielectric properties was conducted. AC breakdown strength (AC-BDS) was analyzed for normal distribution using four methods (Anderson–Darling, Shapiro–Wilk, Ryan–Joiner, and Kolmogorov–Smirnov). In addition, the AC-BDS was analyzed at risk probabilities of 1%, 5%, 10%, and 50% using Weibull distribution functions. Both normal and Weibull distributions were evaluated using the Anderson–Darling (A-D) statistic and p-value. Additionally, the log-normal, gamma, and exponential distributions of AC-BDS were examined by A-D goodness-of-fit test. The hypothesis test results of AC-BDS were fit by normal and Weibull distributions, and the compliance was evaluated by p-value and each method statistics. In addition, the experimental results of AC-BDS were fit by log-normal and gamma distributions, and the goodness-of-fit was evaluated by p-value and A-D testing. On the other hand, exponential distribution was not suitable for p-value and A-D testing. The results showed that the distributions of AC-BDS were the best using log-normal distribution. Meanwhile, statistical analysis results verified the apparent effect of temperature on dielectric properties using a paired t-test. The analysis results of this paper not only contribute to better characterization of epoxy/Al2O3 micro-composites but also introduce a comprehensive approach for performing statistical analysis for electrical insulation materials. [ABSTRACT FROM AUTHOR]

Seismic risk expresses the expected degree of damage and loss following a catastrophic event. An efficient tool for assessing the seismic risk of embankments is fragility curves. This research investigates the influence of embankment's geometry, the depth of rupture occurrence, and the underlying sandy soil's conditions on the embankment's fragility. To achieve this, the response of three highway embankments resting on sandy soil was examined through quasi-static parametric numerical analyses. For the establishment of fragility curves, a cumulative lognormal probability distribution function was used. The maximum vertical displacement of the embankments' external surface and the fault displacement were considered as the damage indicator and the intensity measure, respectively. Damage levels were categorized into three qualitative thresholds: minor, moderate, and extensive. All fragility curves were generated for normal and reverse faults, as well as the combination of those fault types (dip-slip fault). Finally, the proposed curves were verified via their comparison with those provided by HAZUS. It was concluded that embankment geometry and depth of fault rupture appearance do not significantly affect fragility, as exceedance probabilities show minimal differences (<4%). However, an embankment founded on dense sandy soil reveals slightly higher fragility compared to the one founded on loose sand. Differences regarding the probability of exceedance of a certain damage level are restricted by a maximum of 7%. [ABSTRACT FROM AUTHOR]

The size of drops generated by the capillary-driven disintegration of liquid ligaments plays a fundamental role in several important natural phenomena, ranging from heat and mass transfer at the ocean-atmosphere interface to pathogen transmission. The inherent nonlinearity of the equations governing the ligament destabilization leads to significant differences in the resulting drop sizes, owing to small fluctuations in the myriad initial conditions. Previous experiments and simulations reveal a variety of drop size distributions, corresponding to competing underlying physical interpretations. Here, we perform numerical simulations of individual ligaments, the deterministic breakup of which is triggered by random initial surface corrugations. The simulations are grouped in a large ensemble, each corresponding to a random initial configuration. The resulting probability distributions reveal three stable drop sizes, generated via a sequence of two distinct stages of breakup. Four different distributions are tested, volume-based Poisson, Gaussian, Gamma, and Log-Normal. Depending on the time, range of droplet sizes and criteria for success, each distribution has successes and failures. However, the Log-Normal distribution roughly describes the data when fitting both the primary peak and the tail of the distribution while the number of droplets generated is the highest, while the Gamma and Log-Normal distributions perform equally well when fitting the tail. The study demonstrates a precisely controllable and reproducible framework, which can be employed to investigate the mechanisms responsible for the polydispersity of drop sizes found in complex fluid fragmentation scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the optimal experimental planning for multi-level stress testing with Type-II censoring when the test units can be put into coherent systems for the experiment. Based on the notion of system signatures of coherent systems and assuming the lifetimes of the test units follow a distribution in a general log-location-scale family of distributions, the maximum likelihood estimators of the model parameters and the Fisher information matrix are derived. For optimal experimental planning, in addition to some commonly used optimality criteria, such as D-optimality, A-optimality, and V-optimality, we also consider the total time of the experiment and the total time on test. Then, motivated by a real-life application in the reliability study of furniture joints, we focus on using series systems in multi-level stress experiments. The methodology is illustrated by considering lognormal and Weibull distributed test units. Numerical and Monte Carlo simulation studies are used to demonstrate the advantages and disadvantages of using series systems in life-testing experiments. A numerical example based on furniture joints with sensitivity analysis is used to elucidate how the proposed methods can be used in planning a life-testing experiment. Finally, some concluding remarks with some future research directions are provided. [ABSTRACT FROM AUTHOR]

The synthetic Tukey's control chart (denoted by Syn-TCC) applies a single observation in the process monitoring and is relatively robust to outliers. For a complex process, the probability distribution of quality characteristic must be carefully identified and the loss of quality characteristic, which is defined as the deviation from the target value, must be accurately estimated so that the quality state of the process may be more comprehensively described. However, the literature rarely studied the economic design of the Syn-TCC with Taguchi's loss function under non normality. In the present study, it is assumed that the quality characteristic follows a log-normal distribution and Taguchi's asymmetric linear and quadratic loss functions are involved to develop the economic-statistical design of the Syn-TCC for multiple assignable causes. A case study is presented to illustrate the application of this economic-statistical design of the Syn-TCC to an IC package industry. The sensitivity analysis of this case study reveals that a larger production lot size and larger two coefficients of loss functions generally lead to a higher total expected cost. [ABSTRACT FROM AUTHOR]

There is little information which examines and compares climate zones or geology/topography in their relation to soil thickness along mountain slopes, where soil thickness is a possible contributing factor for the increase of sediment wash-off. In this study, the data obtained from handy penetration tests conducted throughout Japan are collected and attached to information on climate zones and geography/topography with the aim of clarifying the difference in soil thickness according to the climate zone and geological classification. The probability distribution of soil thickness was found to fit roughly with the probability density function of a log-normal distribution, regardless of the climate zone or geological age / lithology. A comparison of μ showed that the soil thickness at target sites in the Pacific climate zone, which have high rainfall, was large, at approximately 2.1 m. Meanwhile, the soil thickness was low, at approximately 1.5 m, at target sites in the Setouchi climate zone, which has low rainfall. A comparison of the geology showed that soil thicknesses of sites where the geology consisted of Tertiary and Quaternary sedimentary rocks were high, at approximately 2.1 m and 2.3 m, respectively. This suggests that, in high-precipitation regions, the weathering of rocks is promoted so that the soil layers tend to increase in thickness. [ABSTRACT FROM AUTHOR]

The performance of numerical weather prediction models has improved dramatically recently. However, model biases remain a fundamental limitation prohibiting the direct implementation of model results. There are several ways to describe wind speed data. The Weibull and lognormal distributions are used to obtain the best-fit model for the wind speed data. This study aims to develop a statistical post-processing method based on the distribution-based scaling (DBS) approach, which scales NWP data to fit the distribution derived using recorded wind speed at that site location. The performance of the suggested method was evaluated using four different error measures. The optimal model is anticipated to have the lowest Mean Bias Error (MBE), Mean Absolute Error (MAE), Root Mean square Error (RMSE), and variance (s2) values. It was determined that employing a DBS strategy significantly improved the NWP by at least 75%. [ABSTRACT FROM AUTHOR]

Dating phylogenetic trees to obtain branch lengths in time units is essential for many downstream applications but has remained challenging. Dating requires inferring substitution rates that can change across the tree. While we can assume to have information about a small subset of nodes from the fossil record or sampling times (for fast-evolving organisms), inferring the ages of the other nodes essentially requires extrapolation and interpolation. Assuming a distribution of branch rates, we can formulate dating as a constrained maximum likelihood (ML) estimation problem. While ML dating methods exist, their accuracy degrades in the face of model misspecification, where the assumed parametric statistical distribution of branch rates vastly differs from the true distribution. Notably, most existing methods assume rigid, often unimodal, branch rate distributions. A second challenge is that the likelihood function involves an integral over the continuous domain of the rates, often leading to difficult non-convex optimization problems. To tackle both challenges, we propose a new method called Molecular Dating using Categorical-models (MD-Cat). MD-Cat uses a categorical model of rates inspired by non-parametric statistics and can approximate a large family of models by discretizing the rate distribution into k categories. Under this model, we can use the Expectation-Maximization algorithm to co-estimate rate categories and branch lengths in time units. Our model has fewer assumptions about the true distribution of branch rates than parametric models such as Gamma or LogNormal distribution. Our results on two simulated and real datasets of Angiosperms and HIV and a wide selection of rate distributions show that MD-Cat is often more accurate than the alternatives, especially on datasets with exponential or multimodal rate distributions. [ABSTRACT FROM AUTHOR]

We determined the size distribution of helium droplets produced in a pulsed beam in the condensation regime from the gas phase. Following electron-impact ionization, the mass-to-charge ratios of the positively charged droplets were determined by measuring their kinetic energies and velocities using an electrostatic cylindrical deflector setup. Over a range of different source conditions, we observed bimodal velocity distributions and log-normal size distributions. Our results are similar to those reported for continuous beams, but with mean sizes larger by a factor of around 100. The log-normal size distributions reported here differ strongly from the exponential distributions recently reported for a pulsed beam produced using a different nozzle design. [ABSTRACT FROM AUTHOR]

Tasks of different nature and difficulty levels are a part of people's lives. In this context, there is a scientific interest in the relationship between the difficulty of the task and the persistence need to accomplish it. Despite the generality of this problem, some tasks can be simulated in the form of games. In this way, we employ data from a large online platform, called Steam, to analyze games and the performance of their players. More specifically, we investigated persistence in completing tasks based on the proportion of players who accomplished game achievements. Overall, we present five major findings. First, the probability distribution for the number of achievements is log-normal distribution. Second, the distribution of game players also follows a log-normal. Third, most games require neither a very high degree of persistence nor a very low one. Fourth, players also prefer games that demand a certain intermediate persistence. Fifth, the proportion of players as a function of the number of achievements declines approximately exponentially. As both the log-normal and the exponential functions are memoryless, they are mathematical forms that describe random effects arising from the nature of the system. Therefore our first two findings describe random processes of fragmenting achievements and players while the last three provide a quantitative measure of the human preference in the pursuit of challenging, achievable and justifiable tasks. [ABSTRACT FROM AUTHOR]

Let X be a random variable with finite second moment. We investigate the inequality: P { | X - E [ X ] | ≤ Var (X) } ≥ P { | Z | ≤ 1 } , where Z is a standard normal random variable. We prove that this inequality holds for many familiar infinitely divisible continuous distributions including the Laplace, Gumbel, Logistic, Pareto, infinitely divisible Weibull, Log-normal, Student's t and Inverse Gaussian distributions. Numerical results are given to show that the inequality with continuity correction also holds for some infinitely divisible discrete distributions. [ABSTRACT FROM AUTHOR]

Reliability analysis of mechanical strength could be used for evaluation of wood scrimber properties in this study. Normal, lognormal, and Weibull distributions were used to determine and selected the optimal model for wood scrimber for the first time. The results of reliability analysis indicated that the bending and tensile strength were well fit for normal distribution. Weibull distribution could describe the probability distribution law of compression strength, and lognormal distribution could reflect the probability distribution law of shear strength, respectively. The standard value of each mechanical strength was determined and compared in accordance with two methods. This illustrated that a significant difference between these two methods is evident in the case of modulus of elasticity (MOE), compression strength (CS), and shear strength (SS), while modulus of rupture (MOR) and tensile strength (TS) yielded similar data. The improvement in mechanical strengths was remarkably affected by the increase in density. Moreover, the microstructure of wood scrimber has a good ratio of deformation with respect to density, which can be significantly explained by compressive densification. The results suggest that the deformation ratio increased from 49.75% to 78.67%, which might reflect the variation in macroscopic mechanical strength of wood scrimber. [ABSTRACT FROM AUTHOR]

Nowadays, many cities in China are facing the challenge of returning black and odorous waters during the rainy seasons. Combined sewer overflow (CSO) was one of the critical triggers. In this study, a new method for estimating frequency distribution of the excess rainfall intensity considering double thresholds (ERId in short) was proposed, which is helpful for estimating severity of CSO. For the specific interceptor well, the upper threshold is the design areal unit discharge (the equivalent rainfall intensity) of its upstream combined sewer and the lower one is the design areal unit discharge of its downstream interceptor sewers minus dry weather flow rate. First, rainfall events were divided and the minimum inter-event time (MIET) was set based on the time of concentration of the combined sewer catchment. Second, double-threshold method was used for ERId calculation and sampling for scenario of 30- minute CSO duration. Finally, the empirical frequency of the sampled ERId(30) was calculated by the mathematical expectation formula (Weibull formula) and five functions (doubly censored exponential distribution, exponential function, Gumbel distribution, Weibull distribution and lognormal distribution) were used for comparison to obtain the best theoretical frequency distribution. Results revealed that: (1) The excess rainfall intensity of double thresholds (ERId) is suitable for characterizing CSO. (2) The frequency distribution of ERId was right (positively) skewed. (3) The kurtosis of the ERId samples is not greater than 3 for all the thresholds studied, which indicates that the distribution is thin-tailed. (4) The optimal frequency distribution function for ERId is doubly censored exponential distribution. Highlights: The double-threshold method of ERI was proposed for characterizing CSO. The frequency distribution is right (positively) skewed and thin-tailed. The doubly censored exponential distribution was the optimal one of ERId. [ABSTRACT FROM AUTHOR]

Our research paper introduces a newly developed probability distribution called the transformed MG-extended exponential (TMGEE) distribution. This distribution is derived from the exponential distribution using the modified Frechet approach, but it has a more adaptable hazard function and unique features that we have explained in detail. We conducted simulation studies using two methods: rejection sampling and inverse transform sampling, to produce summaries and show distributional properties. Moreover, we applied the TMGEE distribution to three real datasets from the health area to demonstrate its applicability. We used the maximum likelihood estimation technique to estimate the distribution's parameters. Our results indicate that the TMGEE distribution provides a better fit for the three sets of data as compared to nine other commonly used probability distributions, including Weibull, exponential, and lognormal distributions. [ABSTRACT FROM AUTHOR]

In this paper we study how the expectations of power means behave asymptotically as some relevant parameter approaches infinity and how to approximate them accurately for general nonnegative continuous probability distributions. We derive approximation formulae for such expectations as distribution mean increases, and apply them to some commonly used distributions in statistics and financial mathematics. By numerical computations we demonstrate the accuracy of the proposed formulae which behave well even for smaller sample sizes. Furthermore, analysis of behavior depending on sample size contributes to interesting connections with the power mean of probability distribution. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, we develop two procedures for identifying the dynamic trends in the parameters of length-biased lognormal distribution based on likelihood ratio and modified information criterion. These methods mainly consider the test of the existence of the change point and provide the maximum likelihood estimation of the change point when the change point exists. In addition, the asymptotic distribution of test statistic based on likelihood ratio is derived as an extreme value distribution, while the asymptotic distribution of test statistic based on modified information criterion is derived as a chi-square distribution. And the consistency of parameter estimation is proved. Simulations are conducted to study the performance of the proposed method in terms of power, coverage probabilities and average sizes of confidence sets. The proposed methods are applied to a real data to illustrate the detecting procedures. [ABSTRACT FROM AUTHOR]

Recent observations and simulations reveal that the circumgalactic medium (CGM) surrounding galaxies is multiphase, with the gas temperatures spanning a wide range at most radii, ∼104 K to the virial temperature (∼106 K for Milky Way). Traditional CGM models using simple density profiles are inadequate at reproducing observations that indicate a broad temperature range. Alternatively, a model based on probability distribution functions (PDFs) with parameters motivated by simulations can better match multiwavelength observations. In this work, we use log-normal distributions, commonly seen in the simulations of the multiphase interstellar and circumgalactic media, to model the multiphase CGM. We generalize the isothermal background model by Faerman et al. to include more general CGM profiles. We extend the existing probabilistic models from 1D-PDFs in temperature to 2D-PDFs in density–temperature phase space and constrain its parameters using a Milky Way-like Illustris TNG50-1 halo. We generate various synthetic observables such as column densities of different ions, UV/X-ray spectra, and dispersion and emission measures. X-ray and radio (Fast Radio Burst) observations mainly constrain the hot gas properties. However, interpreting cold/warm phase diagnostics is not straightforward since these phases are patchy, with inherent variability in intercepting these clouds along arbitrary lines of sight. We provide a tabulated comparison of model predictions with observations and plan to expand this into a comprehensive compilation of models and data. Our modelling provides a simple analytical framework that is useful for describing important aspects of the multiphase CGM. [ABSTRACT FROM AUTHOR]

Rainstorm is one of the global meteorological disasters that threaten the safety of transportation infrastructure and the connectivity of transportation system. Aiming to support the resilience assessment of transportation infrastructure in three representative regions: Sichuan–Chongqing, Yangtze River Delta, and Beijing-Tianjin-Hebei-Shandong, rainfall data over 40 years in the three regions are collected, and the temporal distribution of rainfall are analyzed. Prediction equations of rainfall are established. For the purpose of this, the probabilistic density function (PDF) is assigned to the rainfall by fitting the frequency distribution histogram. Using the assigned PDF, the rainfall data are transformed into standard normal space where regression of prediction equations is performed and the prediction accuracy is tested. The results show that: (1) The frequency of rainfall in the three regions follows a lognormal distribution based on which the prediction equations of rainfall can be established in standard normal space. The error of regression shows no remarkable dependence on self-variables, and the significance analysis indicates that the equations proposed in this paper are plausible for predicting rainfalls for the three regions. (2) The Yangtze River Delta region has a higher risk of rainstorm disaster compared to the other two regions according to the frequency of rainfall and the return period of precipitation concentration. (3) Over the period of 1980–2021, the Sichuan–Chongqing region witnessed an increase in yearly rainfall but a decrease in rainstorm disasters, whereas the other two regions experienced a consistent rise in both metrics. [ABSTRACT FROM AUTHOR]

To cope with harsh working conditions, new corrosion-resistant coated steel wires with higher tensile strength have been developed. This study investigates the corrosion characteristics of a new zinc–aluminum alloy-coated steel wire under stress conditions. The particulate corrosion products generated by the oxidation of the coating in the initial stage of corrosion are converted into layer-structured corrosion products at the early stage of corrosion. Moreover, high-stress conditions have a significant influence on the critical conversion time from the coating corrosion stage to the iron matrix corrosion stage. Thus, the uniform corrosion depth (i.e., the mass loss rate) could be fitted with a continuous power function model rather than the previously used two-stage model owing to an ambiguous moment of conversion under stress conditions. The pitting corrosion depth could be fitted with a lognormal distribution in this study. The probability distributions for the aspect ratios of corrosion pits under different stress conditions tended to be consistent. Finally, the block's maximum pitting factor followed a Gumbel distribution with a scale parameter that changed linearly with the stress level and a location parameter related to the square of the stress level. [ABSTRACT FROM AUTHOR]

The class of log-symmetric distributions is a generalization of log-normal distribution and includes some well-known distributions such as log-normal, log-logistic, log-Laplace, log-Cauchy, log-power-exponential, log-student-t, log-slash, and Birnbaum-Saunders distributions. In this paper, several characterization results are obtained for log-symmetric distributions based on moments of some functions of the parent distribution and also on the basis of some properties of order statistics. Specifically, when X is identical in distribution with a decreasing continuous function $ h(X) $ h (X) , then a relationship is established between upper and lower order statistics which is then utilized to construct characterization results for log-symmetric distributions in terms of functions of order statistics. The established results can be used for constructing a goodness-of-fit test for log-symmetric distributions. [ABSTRACT FROM AUTHOR]

Inverse Weibull, lognormal, and inverse Gaussian are some commonly used statistical distributions for modeling positively skewed failure lifetime data. These distributions share some interesting properties among themselves like they all have uni‐modal hazard rates. In this paper, we address the problem of discriminating among these statistical distributions to consider a more appropriate lifetime model. We first consider the complete samples and make use of the maximized log‐likelihood approach for choosing the correct model. We also obtain the expressions for logarithmic of defined test statistics, and associated asymptotic distributions. We then extend our discussion based on the observed sample in the presence of some censoring. We perform a simulation study in both cases to compare the probabilities of correct selection. Furthermore, for a given probability of correct selection and user‐specified protection level, we present a discussion to determine the minimum sample size required to discriminate among the three lifetime models. Finally, two real data sets are analyzed to illustrate the proposed methodology. In our findings, we observed that model parameters and methods of estimating unknown parameters play very important roles in the discrimination process, and sample size and the proportion of censoring become key factors to ensure a high probability of selecting a correct model. [ABSTRACT FROM AUTHOR]

Coarse-grained molecular dynamics simulations are employed to investigate the spatiotemporal evolution of vesicles (polymersomes) through the self-assembly of randomly distributed amphiphilic BAB triblock copolymers with hydrophilic A and hydrophobic B blocks in an aqueous solution. The vesiculation pathway consists of several intermediate structures, such as an interconnected network of copolymer aggregates, a cage of cylindrical micelles, and a lamellar cage. The cage-to-vesicle transition occurs at a constant aggregation number and practically eliminates the hydrophobic interfacial area between the B block and solvent. Molecular reorganization underlying the sequence of morphology transitions from a cage-like aggregate to a vesicle is nearly isentropic. The end-to-end distances of isolated copolymer chains in solution and those within a vesicular assembly follow lognormal probability distributions. This can be attributed to the preponderance of folded chain configurations in which the two hydrophobic end groups of a given chain stay close to each other. However, the probability distribution of end-to-end distances is broader for chains within the vesicle as compared with that of a single chain. This is due to the swelling of the folded configurations within the hydrophobic bilayer. Increasing the hydrophobicity of the B block reduces the vesiculation time without qualitatively altering the self-assembly pathway. [ABSTRACT FROM AUTHOR]

In unsaturated soil mechanics, the soil–water characteristic curve (SWCC) is the most fundamental soil attribute. All seepage analyses require SWCC to generate the pore-water pressure and water content distribution within the soil layers. SWCC is often determined using laboratory procedures. However, the expensive cost, long testing time, and difficulty of the SWCC tests hinder the use of unsaturated soil mechanics in engineering practice. Models for predicting SWCC have been proposed in the literature; however, the equations cannot be applied to soils of a wide variety, and their parameters lack physical significance. This work used a modified lognormal distribution function to generate the equations that best suit the grain-size distribution (GSD) and the model that estimates SWCC for a wide range of soil types. The parameters of the proposed GSD equation have well-defined physical meanings. The model for estimating SWCC was established based on the link between soil pore-size distribution and dry density, void ratio, and saturated water content. The air-entry value of coarse-grained soil is a function of inflection point of SWCC and percentage of coarse particle. The air-entry value of fine-grained soil is a function of saturated water content. Experiments were carried out as part of this study to evaluate the proposed equation as well as its model. The proposed model to estimate SWCC was compared with other models. The proposed model is better than other models in the estimation of SWCC from GSD. [ABSTRACT FROM AUTHOR]

Impedance spectroscopy experiments are able to reveal the fundamental charge transport properties of a wide variety of complex disordered and nano-structured materials provided that appropriate modeling tools are used. In this paper, we present a numerical simulation-based approach to model the dynamical conductivity of networks formed by self-assembled metal nanoparticles. Inter-particle nano-resistance and nano-capacitance are implemented at the nano-scale assuming inter-particle charge transfer and accumulation mechanisms that can be adapted depending on the nature of the nano-particles and the surrounding medium. The actual positions and spatial arrangements of the nanoparticles within the network are taken into consideration, allowing the attributes of percolating conducting routes to be extracted, classified, and compared in terms of path conductance and statistical distribution of path lengths. Our findings are contrasted to those obtained using analytic models, which are commonly used, but rely on strong assumptions about the electric properties of the conducting paths. We address these assumptions and show that in the case of weakly disordered systems, there is a general agreement between numerical simulations and analytic modeling-based approaches. In the case of disordered networks where the nano-particle size and position fluctuations are included, we show that the path length distribution is frequency-dependent and can differ significantly from the lognormal distribution usually assumed in the analytic models. The impedance of individual pathways may be extracted from the numerical simulations; we discovered that the conductance and susceptance of a specific path are frequency-dependent and inversely proportional to the path length only in ordered networks. Strong scattering of conductance values is caused by disorder effects. The developed numerical approach is generic and applies to most nano-devices where charge transport relies on percolation; it allows to bridge the gap between the nano-scale and micro-scale electric characteristics and, thus, permits a deeper understanding of the charge transport properties of nano-structured materials. [ABSTRACT FROM AUTHOR]

The lognormal statistical distribution was used to present the reliable integrated data on the content of various physicochemical forms of tritium in air, natural water, and components of aquatic ecosystems at nuclear facility sites. Statistics of lognormal distributions took into account the left truncation, which reflects the effect of finite sensitivity of measurements. The statistics of lognormal distributions were used to obtain estimates for ecosystems of NPP sites at limited sets of data. Specific activities were estimated for various forms of tritium such as HTO (free water), TFWT (tissue free water tritium), and OBT (organically bound tritium). The measurement results show that the specific activity of tritium in the body in bound forms was, as a rule, higher than its specific activity in free water in the ambient environment. Equilibrium concentration ratios (CRs) (partition coefficients of hydrogen) ranged from 1 to about 20. The results obtained by the Radium Institute research team agree with those obtained by the researchers from Canada and France for the specific activity of tritium in different chemical forms in environmental samples. [ABSTRACT FROM AUTHOR]

Exploring the realm of extreme weather events is indispensable for various engineering disciplines and plays a pivotal role in understanding climate change phenomena. In this study, we examine the ability of 10 probability distribution functions—including exponential, normal, two- and three-parameter log-normal, gamma, Gumbel, log-Gumbel, Pearson type III, log-Pearson type III, and SQRT-ET max distributions—to assess annual maximum 24 h rainfall series obtained over a long period (1972–2022) from three nearby meteorological stations. Goodness-of-fit analyses including Kolmogorov–Smirnov and chi-square tests reveal the inadequacy of exponential and normal distributions in capturing the complexity of the data sets. Subsequent frequency analysis and multi-criteria assessment enable us to discern optimal functions for various scenarios, including hydraulic engineering and sediment yield estimation. Notably, the log-Gumbel and three-parameter log-normal distributions exhibit superior performance for high return periods, while the Gumbel and three-parameter log-normal distributions excel for lower return periods. However, caution is advised regarding the overuse of log-Gumbel, due to its high sensitivity. Moreover, as our study considers the application of mathematical and statistical methods for the detection of extreme events, it also provides insights into climate change indicators, highlighting trends in the probability distribution of annual maximum 24 h rainfall. As a novelty in the field of functional analysis, the log-Gumbel distribution with a finite sample size is utilised for the assessment of extreme events, for which no previous work seems to have been conducted. These findings offer critical perspectives on extreme rainfall modelling and the impacts of climate change, enabling informed decision making for sustainable development and resilience. [ABSTRACT FROM AUTHOR]

The determination of the so-called design block is one of the central elements of the Austrian guideline for rockfall protection ONR 24810. It is specified as a certain percentile (P95–P98, depending on the event frequency) of a recorded block size distribution. Block size distributions may be determined from the detachment area (in situ block size distribution) and/or from the deposition area (rockfall block size distribution). Deposition areas, if present, are generally accessible and measurable without technical aids. However, most measuring methods are subjective, uncertain, not verifiable, or inaccurate. Also, rockfall blocks are often fragmented due to the preceding fall process. The in situ block size distribution is (also) required for meaningful rockfall modelling. The statistical method seems to be the most efficient and cost-effective method to determine in situ block size distributions with many blocks within the whole range of block sizes. In the current literature, joint properties are often described by the lognormal and exponential distribution functions. Today, we can model synthetic rock masses on the basis of discrete fracture networks. They statistically describe the geometric properties of the joint sets. This way, we can carry out exact rock mass block surveys and determine in situ block size distributions. We wanted to know whether the in situ block size distributions derived from the synthetic rock mass models can be described by probability distribution functions, and if so, how well. We fitted various distribution functions to three determined in situ block size distributions of different lithologies. We compared their correlations using the Kolmogorov–Smirnov test and the mean-squared error method. We show that the generalized exponential distribution function best describes the in situ block size distributions across various lithologies compared to 78 other distribution functions. This could lead to more certain, accurate, verifiable, holistic, and objective results. Further investigations are required. [ABSTRACT FROM AUTHOR]

LiDAR-based digital terrain models (DTMs) represent an advance in the investigation of small-scale geomorphological features, including dolines of karst terrains. Important issues in doline morphometry are (i) which statistical distributions best model the size distribution of doline morphometric parameters and (ii) how to characterize the volume of dolines based on high-resolution DTMs. For backward compatibility, how previous datasets obtained predominantly from topographic maps relate to doline data derived from LiDAR is also examined. Our study area includes the karst plateaus of Aggtelek Karst and Slovak Karst national parks, whose caves are part of the UNESCO World Heritage. To characterize the study area, the relationships between doline parameters and topography were studied, as well as their geological characteristics. Our analysis revealed that the LiDAR-based doline density is 25% higher than the value calculated from topographic maps. Furthermore, LiDAR-based doline delineations are slightly larger and less rounded than in the case of topographic maps. The plateaus of the study area are characterized by low (5–10 km−2), moderate (10–30 km−2), and medium (30–35 km−2) doline densities. In terms of topography, the slope trend is decisive since the doline density is negligible in areas where the general slope is steeper than 12°. As for the lithology, 75% of the dolines can be linked to Wetterstein Limestone. The statistical distribution of the doline area can be well modeled by the lognormal distribution. To describe the DTM-based volume of dolines, a new parameter (k) is introduced to characterize their 3D shape: it is equal to the product of the area and the depth divided by the volume. This parameter indicates whether the idealized shape of the doline is closer to a cylinder, a bowl (calotte), a cone, or a funnel shape. The results show that most sinkholes in the study area have a transitional shape between a bowl (calotte) and a cone. [ABSTRACT FROM AUTHOR]

Accurate estimation of activity durations is a critical project scheduling step. If abundant data are available for activity durations, then distribution fitting is straightforward. However, if sample sizes are small, then choosing an appropriate theoretical distribution for activity duration is challenging. In this study, we propose a methodology for experimenting with the impact of sample size on the accuracy of the estimated duration of a stochastic project network. We synthesized a total of 3,264 stochastic project networks and estimated the true project duration distribution for each network using large-sample Monte Carlo simulation. We varied the sample size per activity and investigated how the choice of theoretical distribution (normal, beta, triangular, and lognormal) for estimated activity durations impacted the accuracy of the estimated project duration distribution. We find that the best choice for a theoretical activity duration distribution highly depends on the sample size. For sample sizes below 50, we find that not much is gained from the common practice of putting extensive effort into selecting best-fit theoretical distributions compared to simply using normal distributions. [ABSTRACT FROM AUTHOR]

It has been known for a long time that (1) when graphs of income amount on income relative rank for two income distributions intersect twice, three "transfer groups" are generated, with the poorest and richest both gaining under the same alternative income distribution and the middle group losing; and (2) the linear income tax system satisfies three fundamental principles of tax justice, namely, that as pretax income increases, three quantities should also increase--posttax income, tax amount, and tax rate. This paper links those two ideas, suggesting that the linear income tax system may be the natural and most effective way to guard against poverty reduction policies which, while helping the poorest, as urged by Rawls, may harm the middle, contributing to the weakening of the middle class, thought at least since Aristotle to be the backbone of society. This paper illustrates the two approaches with one initial distribution and three alternative final distributions, contrasting their minimum, median, proportion below the mean, and inequality. It also shows how to guard the linear income tax system against violating the tax amount principle of tax fairness when there is an injection of resources (e.g., from deficit spending or oil revenues) and how to empirically estimate the parameters (e.g., the marginal tax rate) of the linear income system that the population will regard as fair. [ABSTRACT FROM AUTHOR]

Understanding joints is becoming increasingly important in South Korea owing to the development of plans for high-level waste disposal. This study examined drill cores to assess the morphology of joints in five areas with different rock types. The depths and dip angles of 14,169 joints were measured, and the joints were then classified based on their dip angles. Joint spacings within each set were statistically analyzed and fitted to five statistical distribution models: double Weibull, exponential, generalized log-logistic, gamma, and lognormal. Results for each given type of rock showed similar dip angles but varying depths. The observed joint spacings were most accurately fitted using the lognormal distribution. The results of this study will provide insights into the distributions of joints in South Korea and can be used in numerical modeling and stability assessments. [ABSTRACT FROM AUTHOR]

Demand side management (DSM) is widely utilized in smart grid for its reliable features, flexibility, and cost benefits that it offers to customers on reduction of the energy bill. In the smart grid, demand response aggregator, power customers, and utility operator all strive to increase their individual profits. However, it is extremely challenging to guarantee profits for all of the candidates simultaneously. In this paper, these criteria are employed to execute a problem with multiple objectives by combining the concept of DSM and dynamic economic emission dispatch considering uncertainties of renewable energy sources (RESs). The uncertainties of RESs can bring adverse effects on the grid operator. Thus, Weibull probability distribution function and lognormal probability distribution function are used to model the uncertainties of wind speed and solar irradiation, respectively, in this paper. Further, the multi-objective improved DSM scheme is optimized by Class Topper optimization algorithm. The objective here is to optimally schedule load demand and generation pattern simultaneously to improve load factor, minimize electricity bill and maximize the profits of all candidates of the day-ahead electricity market simultaneously. Error in the load forecasting model may lead to growing operational cost of energy generation. In this paper, a machine learning model using linear regression is used for short-term load forecasting (STLF) to forecast day-ahead load demand. The simulation results show the importance of the improved DSM scheme and the advantage of STLF, which further help to improve the economy and efficiency of the smart grid. [ABSTRACT FROM AUTHOR]

Coarse-grained molecular dynamic simulations are employed to investigate the spatiotemporal evolution of vesicles (polymersomes) via self-assembly of randomly distributed amphiphilic diblock copolymers PB-PEO (Poly(Butadiene)-b-Poly(Ethylene Oxide)) in water. The vesiculation pathway consists of several intermediate structures, such as spherical/rodlike aggregates, wormlike micelles, lamellae, and cavities. The lamella-to-vesicle transition occurs at a constant aggregation number and is accompanied by a reduction in the solvent-accessible surface area. Simulation predictions are in qualitative agreement with the mechanism of vesicle formation in which the unfavorable hydrophobic interactions between water molecules and polymer segments, along the edge of the lamella, are eliminated at the expense of gaining curvature energy. However, rod–lamella–vesicle transition is accompanied by an increase in copolymer packing density. Hence, the change in the surface area accompanying vesiculation predicted by the simulations is significantly lower than theoretical estimates. Changes in information entropy, quantified by the expectation of the logarithm of the probability distribution function of the segmental stretch parameter s, defined as the difference between the maximum and instantaneous segmental extension, are statistically insignificant along the vesiculation pathway. For rods, lamellae, and polymersomes, s follows a log normal distribution. This is explained based on the configurational dynamics of a single diblock chain in water. [ABSTRACT FROM AUTHOR]

The load spectrum is an important component in the reliability testing of machining centers. The statistical characteristics of a load must be accurately estimated to evaluate the capacity of a machining center to withstand the applied load. Due to the complexity of the processing technology, diversity of the processed materials, and uncertain factors, several types of cutting loads present single or bimodal distributions for which the conventional one-component probability density function (PDF) is inappropriate. Mixture distributions are regarded as an appropriate alternative for modeling such load data. In addition, parameter estimation for these mixture models requires an advanced optimization method, which takes a substantial amount of time to process. However, machining centers typically involve a variety of processing methods, each giving rise to various load types, resulting in a significant increase in the amount of calculation in parameter estimation. Accordingly, rapid and accurate selection of the best matching hybrid model is a great challenge. To solve this problem, a method for compiling a two-component distribution function based on the linear moment ratio diagram (L-MRD) method is proposed to rapidly and accurately model multiple types of load distributions. First, the one-component and the two-component mixture models consisting of normal distribution (Norm), Gumbel or extreme value type I (E), generalized extreme value (GEV), Pearson type III (P3), and 3-parameter Lognormal (LN3) distributions are selected as candidate models, and the mean and amplitude are applied to milling total eight load sets. Thereafter, the best two-component hybrid model for each load set is determined by taking the estimated value of the load sample data in L-MRD and the relative position of the candidate distribution in L-MRD as the basis for selecting the best matching distribution. The estimation of the parameter of the mixture models is obtained with the least-squares and maximum likelihood methods. The optimization of the objective functions related to these estimation methods is carried out with a genetic algorithm (GA) that is more adapted to mixture distributions. Finally, the results obtained with the L-MRD are compared with those obtained with goodness-of-fit statistics through model selection criteria. Analysis results indicate that L-MRD quickly and effectively selects the optimal mixture distribution component type on a single graph and offers more information than a goodness-of-fit criterion because it provides knowledge about such characteristics as the skewness and kurtosis of the load data samples. In addition, the mixture models improve the modeling flexibility, minimize statistical errors, enhance the fitting accuracy, and generate load spectra that better reflect the actual load characteristics. [ABSTRACT FROM AUTHOR]

In data analysis, we cannot expect the data under study to always follow a symmetric probability distribution; they can have a skewed probability distribution. Modeling skewed data is a challenging task for data scientists. A mixture of probability distributions is a better option for modelling skewed data. In this study, we generated a few mixtures of probability distributions using the exponential as the first fixed component and Gompertz, Lindley, and log-normal distributions as the second component for modelling skewed data. We also examined the characteristics of mixed probability distributions. The maximum likelihood method was used to estimate the unknown parameters. As a result, all three mixture models have a right-skewed pattern, which provides a better fit than existing distributions. Finally, we used real-time datasets to model skewed data. [ABSTRACT FROM AUTHOR]

Buildings located on hill slopes are subjected to additional effects under seismic action compared with those on flat ground. This article presents Incremental Dynamic Analyses of coupled building‐slope systems incorporating topographic amplification, nonlinear slope movement and irregular structural configuration of hill‐side buildings. Two different stable slopes, supporting single and multiple adjacent ductile moment resisting reinforced concrete frame buildings with step‐back configuration, prevalent in Indian and Chinese hilly regions, are modelled and analyzed using the finite element software ABAQUS. A suite of 21 ground motions is incrementally scaled and used to compute the seismic response of the coupled system. Fragility curves for different damage states, derived as lognormal probability distributions in terms of three different Intensity Measures (IMs) and damage probabilities of the considered buildings, are derived and compared. The spectrum‐based IMs (e.g., spectral acceleration at fundamental period, and average of the spectral acceleration over a period range) result in lower record‐to‐record variability, compared with the peak ground acceleration as the IM. The results reveal that ignoring the effect of slope significantly underestimates the fragility for all the damage states. [ABSTRACT FROM AUTHOR]

Various statistical distributions, such as Weibull, log-normal, and exponential functions, are frequently employed to interpret the dielectric breakdown (BD) strength data of insulating materials, including cross-linked polyethylene, low-density polyethylene, polypropylene (PP), and polyethylene. This study aimed to determine a suitable statistical distribution for analyzing the dielectric BD strength data of PP insulators before and after thermal degradation. Dielectric BD strength tests were conducted on thermally deteriorated PP insulators under various degradation conditions. Additionally, a coefficient of determination was employed to assess the compatibility between the dielectric BD strength data and the statistical distribution of PP insulators before and after thermal degradation. The test results indicate that the coefficient of determination for alternating current BD strength data was 0.955 in the log-normal distribution before degradation and 0.929 in the Weibull distribution after degradation. Consequently, in the analysis of the PP insulation breakdown data, the log-normal distribution was found to be suitable for data before degradation, while the Weibull distribution was deemed suitable for data after degradation. These results can lead to lower errors in the power system design process, enhancing reliability when analyzing the BD strength data of insulation materials. [ABSTRACT FROM AUTHOR]

Threshold selection is challenging when analyzing tail data with a generalized Pareto distribution. Data below the threshold was not used in the model, resulting in incomplete characterization of the whole data. This paper applied the Gamma distribution, Weibull distribution, and lognormal distribution to fit the central data separately, and a generalized Pareto distribution (GPD) was used to analyze the tail data. In such composite models, the thresholds are estimated directly as parameters. We proposed an empirical distribution function-based parameter estimation method. The absolute value of the difference between the empirical distribution function and the composite distribution function was used as a loss function to obtain an estimate of the parameter. This parameter estimation method is suitable for complex multiparameter distributions. The estimation method based on the empirical distribution function was verified to be feasible through simulation studies. The composite model and the estimation method based on the empirical distribution function were applied to study the earthquake magnitude data to provide a reference for earthquake hazard analysis. [ABSTRACT FROM AUTHOR]

Parking duration analysis is an important aspect of evaluating parking demand. Identifying accurate distribution characteristics of parking duration can not only enhance parking efficiency and parking facility planning, but also provide essential support for parking delicacy management. Previous studies have proposed various statistical distributions to depict parking duration data. However, it is difficult to find a certain type of distribution to describe the characteristics of parking duration in diverse parking facilities, since model uncertainty is caused by stochastic parking behaviors and diverse parking environments. To address the model uncertainty, a Bayesian model averaging (BMA) was applied to integrate the advantages of different statistical distributions to depict parking duration characteristics. The parking dataset was collected from a commercial parking lot in Chengdu, China, and the dataset was categorized into two groups (i.e., temporary users and long-term users) to analyze. A set of statistical distributions was chosen as candidate models, and their corresponding unknown parameters were estimated. The posterior model probability for each candidate model was calculated according to the goodness-of-fit (GOF) metric. The findings of the study illustrate that there is no universally applicable distribution form (e.g., log-normal distribution) to depict the parking duration distribution for both user types, whereas the BMA approach assigns weights to candidate models and always provides an accurate description of the parking duration characteristics. The parking duration analysis is useful for improving parking management strategies and optimizing parking pricing policies. [ABSTRACT FROM AUTHOR]

In a one-way design with unknown and unequal error variances, we are interested in testing the null hypothesis H 0 : μ 1 = μ 2 = ⋯ = μ k against the ordered alternative H 1 : μ 1 ≤ μ 2 ≤ ⋯ ≤ μ k (with at least one strict inequality). We propose the likelihood ratio test (LRT) as well as two Min-T tests (Min-T and AMin-T) and study their asymptotic behaviour. For better finite sample properties, a parametric bootstrap procedure is used. Asymptotic accuracy of the parametric bootstrap is established. Simulation results show that all the tests control the nominal level in case of small, moderate, and highly unbalanced sample sizes. This even holds for combinations with large variances. However, the asymptotic likelihood ratio test (ALRT) achieves the nominal size only for large samples and k = 3 . Power comparisons between LRT and Min-T test show that the LRT has more power than Min-T. However, the Min-T test is easier to use as it does not require evaluation of MLEs. Similar observations are made while comparing ALRT and AMin-T test. The robustness of these tests under departure from normality is also investigated by considering five non-normal distributions (t-distribution, Laplace, exponential, Weibull, and lognormal). When high variances are combined with small or highly unbalanced sample sizes, the tests are observed to be robust only for symmetric distributions. If variances of groups are equal and sample sizes of each group are at least 10, the proposed tests perform satisfactorily for symmetric and skewed distributions. R packages are developed for all tests and a practical example is provided to illustrate their application. [ABSTRACT FROM AUTHOR]

Risk evaluation for fatigue failure of the engineering components is an important aspect of the engineering design. Weibull distributions are often used in preference to the log-normal distribution to analyze probability aspects of fatigue results. This study presents a probabilistic model for calculating Weibull distribution parameters to reduce the effect of percentage discretization error of experimental fatigue life and R–S–N curves for three reliability levels. By considering any result of standard fatigue test as an equivalent Weibull distribution, artificial data are generated and the accuracy of common Weibull distribution model can be improved. The results show error reduction in the Kolmogorov–Smirnov test and R-square values. Also, the Basquin model is used for different reliability levels with the same error order for risk evaluation of fatigue failure. The coefficient of variation for fatigue life increases at higher stress levels and has a linear relation with stress level for a high-cycle fatigue regime. [ABSTRACT FROM AUTHOR]

This review presents the main results of the author's study, obtained as part of the post-doctoral (habilitation) dissertation entitled "Research on Statistical Distributions of Navigation Positioning System Errors", which constitutes a series of five thematically linked scientific publications. The main scientific aim of this series is to answer the question of what statistical distributions follow the position errors of navigation systems, such as Differential Global Positioning System (DGPS), European Geostationary Navigation Overlay Service (EGNOS), Global Positioning System (GPS), and others. All of the positioning systems under study (Decca Navigator, DGPS, EGNOS, and GPS) are characterised by the Position Random Walk (PRW), which means that latitude and longitude errors do not appear randomly, being a feature of the normal distribution. The research showed that the Gaussian distribution is not an optimal distribution for the modelling of navigation positioning system errors. A higher fit to the 1D and 2D position errors was exhibited by such distributions as beta, gamma, and lognormal. Moreover, it was proven that the Twice the Distance Root Mean Square (2DRMS(2D)) measure, which assumes a priori normal distribution of position errors in relation to latitude and latitude, was smaller by 10–14% than the position error value from which 95% fixes were smaller (it is known as the R95(2D) measure). [ABSTRACT FROM AUTHOR]

Tropospheric ozone or ground-level ozone, mainly found near ground level, has adverse effects on human health. Distribution fitting is useful for predicting the probability, or forecasting the frequency of recurrence, of a phenomenon in a specific period of time. This study aimed to find the best fit distribution of ground-level ozone for specific industrial, rural, and suburban areas of monitoring locations in Malaysia, which were Kuala Terengganu, Jerantut, and Banting. Secondary data from 2017 to 2020 used in this study were obtained from the Department of Environment Malaysia (DoE). This study employed eight probability distributions namely Weibull, gamma, lognormal, logistic, log-logistic, Birnbaum-Saunders, Nakagami, and inverse Gaussian. The method of moments was used to estimate the parameters for each distribution and the best distribution can be used for predicting the return period of the concentration. The descriptive statistics analysis showed that ground-level ozone reached the highest peak at 1400 and 1500 hours, due to the UV radiation from sunlight, while the lowest concentration reading was at 0700 hours at all monitoring locations. By comparing the analysis of the eight distributions, Nakagami was found to be the best fit distribution to the actual monitoring data for Kuala Terengganu, Jerantut, and Banting stations from 2017 to 2020. As a result, this study suggests that the Nakagami distribution be used to predict exceedances and return periods, based on the performance indicators. Thus, it can take the place of the typical distributions employed in fitting the distribution of air pollutants, such as the lognormal distribution and the gamma distribution. [ABSTRACT FROM AUTHOR]

Colloidal clogging is typically studied in pores with constrictions arranged in parallel or series. In these systems, clogging statistics are governed by Poisson processes; the time interval between clogging events exhibits an exponential distribution. However, an entirely different phenomenon is observed in a gently tapered pore geometry. Unlike in non-tapered constrictions, rigid particles clogging tapered microchannels form discrete and discontinuous clogs. In a parallelized system of tapered microchannels, we analyze distributions of clog dimensions for different flow conditions. Clog width distributions reveal a lognormal process, arising from concurrent clogging across independent parallel microchannels. Clog lengths, however, which are analogous to growth time, are exponentially distributed. This indicates a Poisson process where events do not occur simultaneously. These two processes are contradictory: clogging events are statistically dependent within each channel, while clogs grow simultaneously across independent channels. The coexistence of Poisson and lognormal processes suggests a transient Markov process in which clogs occur both independently of, and dependently on, other clogs. Therefore, discussions of the stochastic character of clogging may require holistic consideration of the quantities used to assess it. This study reveals small adjustments to pore spaces can lead to qualitative differences in clogging dynamics, suggesting the importance of geometry. [ABSTRACT FROM AUTHOR]

Aiming at establishing the transient flow characteristics of gas–liquid two-phase flow in high-undulation water pipelines, based on the bubble distribution law measured using physical tests, the bubble distribution law function was input into the hump-pipe fluid domain model, and CFD numerical simulation was carried out for different flow rates and different air contents. The CLSVOF two-phase flow model and the RNG k-ε turbulence model were used to analyze the flow pattern evolution and pressure pulsation propagation in the process of gas–liquid two-phase flow through a hump pipe. The results show that the bubble size has a lognormal distribution, the equivalent diameter is between 3 mm and 10 mm, and the evolution of the flow pattern in the hump pipe is complex and violent. In the horizontal pipe section, there are three main flow patterns: bubble flow, wavy flow and segment plug flow. In the vertical pipe, there are two main flow patterns, slug flow and churning flow, and the flow pattern is affected by the flow rate and the air content rate. When air bubbles or air pockets in the pipeline flow through a certain area, this leads to a steep increase and decrease in the pressure pulsation amplitude in the region, and the pressure fluctuation is extremely frequent. Compared with the water flow rate, the air content is the main factor affecting the relative pressure pulsation amplitude under the condition of a 0.15-air content operating mode, which is generally approximately two to six times that of the 0-air content operating mode. The results of the research should facilitate the prediction of stagnant gas pipeline system bursts and water hammer protection, providing a theoretical basis and calculation parameters. [ABSTRACT FROM AUTHOR]

The extent and occurrence of extremely low-flow events are necessary to determine the minimum river flow. Since the true probability distribution is usually not known, the best fitting distribution function describing the low flow in the catchment is important for reliable estimation of low flow and its frequency. The Temsa River is one of the most important tributaries of the Abay River Basin in Ethiopia and has a high ecological value for the country that can be affected by land cover changes. Climate influences watershed development, while landscape features control the accumulation and release of water over time, influencing stream flow, such as low flow. Therefore, analyzing the state of river discharge is important for the economic management of water resources. Rapid population growth has raised serious concerns about the adequacy of the Temsa River's future water intake in terms of quantity and quality. However, future water resources planning requires information on water flow variability and trends. The aim of this study is to identify and analyze the existing Temsa watersheds and their current status based on river water data collected by the Ethiopian Ministry of Water and Energy from 1997 to 2021 GC. Analysis focused on daily flow, mean annual flow, mean monthly flow, and consecutive 7-day mean minimum flow were included in the model. Methods for trend detection and quantification were the Mann–Kendall test (MK) and Sen's slope estimator (SS). The results of the MK and SS tests indicate the existence of a trend of statistical significance. The study shows a positive trend for two models and a negative trend for the other two models. The daily discharge analysis and the annual average flow analysis show a decreasing trend and the second model shows an increasing trend. BFI results show that the proportion of groundwater in the watershed is moderate, 73.6%, and the lognormal distribution fits the frequency analysis data. [ABSTRACT FROM AUTHOR]