Search

The lognormal moment sequence is considered. Using the fractional moments technique, it is first proved that the lognormal has the largest differential entropy among the infinite positively supported probability densities with the same lognormal-moments. Then, relying on previous theoretical results on entropy convergence obtained by the authors concerning the indeterminate Stieltjes moment problem, the lognormal distribution is accurately reconstructed by the maximum entropy technique using only its integer moment sequence, although it is not uniquely determined by moments. [ABSTRACT FROM AUTHOR]

In this paper we consider a special kind of semicontinous distribution. We try to concern with the situation where the probability of zero observation is associated with the location and scale parameters in lognormal distribution. We first propose a goodness-of-fit test to ensure that the data can be fit by the associated delta-lognormal distribution. Then we define the updated fiducial distributions of the parameters and establish the results that the confidence interval has asymtotically correct level while the significance level of the hypothesis testing is also asymtotically correct. We propose an exact sampling method to sample from the updated fiducial distribution. It can be seen in our simulation study that the inference on the parameters is largely improved. A real data example is also used to illustrate our method. [ABSTRACT FROM AUTHOR]

This study develops empirical fragility curves for concrete and masonry buildings in Haiti, utilizing data from the 2021 earthquake. A dataset of 3527 buildings from the StEER database, encompassing a diverse range of building types, is used. These buildings types include reinforced concrete structures with masonry infills, confined masonry buildings, reinforced masonry bearing walls, and unreinforced masonry bearing walls. Shakemaps from the USGS are utilized to assess the earthquake's intensity at each building, with the peak ground acceleration (PGA) as the intensity measure. Damage is classified into five distinct states: no damage, minor, moderate, severe, and partial or total collapse. For each of these states, the corresponding probabilities of exceedance are calculated, and log-normal cumulative distribution functions were fitted to those data to produce empirical fragility curves. The results show a notable similarity in performance among the four types, each having high probability of failure even under low-intensity earthquakes. Total fragility curves (including all four building types) are developed subsequently and they are convolved to the probabilistic seismic hazard map of Haiti to assess the seismic risk. This includes estimating the annual probability of partial/total collapse and the probability of partial/total collapse in the event of 475-year and 2475-year earthquakes. The results indicate a significant risk, with up to 64% probability of collapse in certain areas for the 2475-year earthquake and a probability of collapse of 15% for a 475-year earthquake. These findings underscore the critical vulnerability of Haiti's buildings to seismic events and the urgent need for their retrofit. [ABSTRACT FROM AUTHOR]

The article proposes a procedure for selecting the blur factor of kernel functions for nonparametric density estimation of a one-dimensional random variable given large amounts of statistical data, for example, obtained via the remote sensing of natural objects. The proposed procedure uses regression density estimation. A procedure is presented for synthesizing a regression density estimate. The estimate synthesis is based on the original sample compression by decomposing the range of a random variable. To this end, the Heinhold-Gaede rule and a formula for choosing the optimal number of sampling intervals are applied. The article considers two approaches to selecting the blur factor of regression density estimation using the conventional method and that proposed by the authors to optimize nonparametric density estimation. The conventional method for optimizing nonparametric density estimation is based on minimizing its standard deviation. In the proposed method, the choice of the blur factors of kernel functions relies on the conditions for the minimum approximation error of regression density estimation. The article analyzes the approximation properties of regression density estimation using two optimization methods. The conditions of their competence in estimating the probability densities of random variables following lognormal distribution are established. The results obtained for a one-dimensional random variable can be used to optimize the regression density estimation of a multi-dimensional random variable. [ABSTRACT FROM AUTHOR]

Copyright of Nuclear Safety is the property of Nuclear & Radiation Safety Center and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Non-orthogonal multiple access (NOMA) is an emerging multiple access technique for future generation wireless networks. Owing to the wide applicability of NOMA, precise expressions for the outage performance under various fading conditions are very much needed. The literature on the outage analysis of NOMA systems is extensive. However, a unified approach is required to test the outage performance of NOMA under various impairments as well as fading scenarios. Hence, in this paper we provide a unique procedure to evaluate the outage probability of downlink-NOMA and preciseness in the derived expressions is achieved by including error in channel state information and successive interference cancellation (SIC), intra- and inter-cell interference. The outage probability is derived over (i) homogeneous fading channels: Rayleigh and Nakagami-m faded distributions with and without log-normal shadowing, Rician fading, and (ii) non-homogeneous fading channels: α - μ , η - μ , α - η - μ , κ - μ and α - κ - μ shadowed distributions. The numerical results are evaluated by varying different fading parameters, error in channel estimation and SIC, and number of interferers. The impact of shadowing on the outage performance of NOMA is also analyzed. The obtained analytical results are validated with simulated results. [ABSTRACT FROM AUTHOR]

The coefficient of quartile variation is a valuable measure used to assess data dispersion when it deviates from a normal distribution or displays skewness. In this study, we focus specifically on the delta-lognormal distribution. The lognormal distribution is characterized by its asymmetrical nature and comprises exclusively positive values. However, when these values undergo a logarithmic transformation, they conform to a symmetrical (or normal) distribution. Consequently, this research aims to establish confidence intervals for the difference between coefficients of quartile variation within lognormal distributions incorporating zero values. We employ the Bayesian, generalized confidence interval, and fiducial generalized confidence interval methods to construct these intervals, involving data simulation using RStudio software. We evaluate the performance of these methods based on coverage probabilities and average lengths. Our findings indicate that the Bayesian method, employing Jeffreys' prior, performs well in low variability, while the generalized confidence interval method is more suitable for higher variability. Therefore, we recommend using both approaches to construct confidence intervals for the difference between the coefficients of the quartile variation in lognormal distributions that include zero values. Furthermore, we apply these methods to rainfall data in Thailand to illustrate their alignment with actual and simulated data. [ABSTRACT FROM AUTHOR]

Given a distribution of earthquake-induced seafloor elevations, we present a method to compute the probability of the resulting tsunamis reaching a certain size on shore. Instead of sampling, the proposed method relies on optimization to compute the most likely fault slips that result in a seafloor deformation inducing a large tsunami wave. We model tsunamis induced by bathymetry change using the shallow water equations on an idealized slice through the sea. The earthquake slip model is based on a sum of multivariate log-normal distributions, and follows the Gutenberg-Richter law for seismic moment magnitudes ranging from 7 to 9. For a model problem inspired by the Tohoku-Oki 2011 earthquake and tsunami, we quantify annual probabilities of differently sized tsunami waves. Our method also identifies the most effective tsunami mechanisms. These mechanisms have smoothly varying fault slip patches that lead to an expansive but moderately large bathymetry change. The resulting tsunami waves are compressed as they approach shore and reach close-to-vertical leading wave edge close to shore. [ABSTRACT FROM AUTHOR]

Shared frailty models, that is, hazard regression models for censored data including random effects acting multiplicatively on the hazard, are commonly used to analyze time-to-event data possessing a hierarchical structure. When the random effects are assumed to be normally distributed, the cluster-specific marginal likelihood has no closed-form expression. A powerful method for approximating such integrals is the adaptive Gauss-Hermite quadrature (AGHQ). However, this method requires the estimation of the mode of the integrand in the expression defining the cluster-specific marginal likelihood: it is generally obtained through a nested optimization at the cluster level for each evaluation of the likelihood function. In this work, we show that in the case of a parametric shared frailty model including a normal random intercept, the cluster-specific modes can be determined analytically by using the principal branch of the Lambert function, W 0 . Besides removing the need for the nested optimization procedure, it provides closed-form formulas for the gradient and Hessian of the approximated likelihood making its maximization by Newton-type algorithms convenient and efficient. The Lambert-based AGHQ (LAGHQ) might be applied to other problems involving similar integrals, such as the normally distributed random intercept Poisson model and the computation of probabilities from a Poisson lognormal distribution. [ABSTRACT FROM AUTHOR]

The bivariate probability distribution of significant wave heights and mean wave periods has an indispensable guiding role in the implementation of offshore engineering, which has attracted great attention. This work gives a new bivariate method to describe the bivariate distribution of significant wave height and mean wave period at the NanJi, BeiShuang, and XiaoMaiDao stations from 2018 to 2020. A mixed lognormal distribution is used for univariate probability analysis of wave data, and the method of connecting two mixed lognormal distributions with copula functions is applied to construct bivariate distribution. The results show that compared with Weibull and lognormal distributions, the mixed lognormal distribution shows good performance in fitting marginal distributions. In the bivariate probability analysis, the conditional model overestimates the probability of lower wave heights, and the bivariate function model has a poor fitting effect in the region with larger periods. In contrast, the copula model based on mixed lognormal distribution is more suited to describe the joint distribution of significant wave height and mean wave period. [ABSTRACT FROM AUTHOR]

For the estimation of left and right-tail probabilities and the pdf of the sum of exchangeable lognormal random vectors a new conditional Monte Carlo (CMC) algorithm is developed. It removes the randomness of the sum of all input variables and is simple and fast. For estimating the left-tail probabilities the CMC algorithm is logarithmically efficient. A further improvement of the algorithm by removing also the randomness of the radius of the normal input using close to optimal one dimensional importance sampling, results in the CMC.RCMC algorithm. For the sum of independent and identically distributed (i.i.d.) and exchangeable lognormal vectors it is the first algorithm that has bounded relative error for the left-tail probabilities. The CMC.RCMC algorithm is logarithmically efficient for the right-tail probabilities. Numerical experiments verify that it has a very good performance for all left-tail estimation problems and a good performance for the right tail for probabilities not smaller than 10 - 10 . When estimating the pdf the relative errors observed are all very close to those of the corresponding probability estimates. [ABSTRACT FROM AUTHOR]

In this paper, we study the inferences of the difference of medians for two independent log-normal distributions. These methods include traditional methods such as the parametric bootstrap approach, the normal approximation approach, the method of variance estimates recovery approach, and the generalized confidence interval approach. The simultaneous confidence intervals for the difference in the median for more than two independent log-normal distributions are also discussed. Our simulation studies evaluate the performances of the proposed confidence intervals in terms of coverage probabilities and average lengths. We find that the parametric bootstrap approach would be a suitable choice for smaller sample sizes for the two independent distributions and multiple independent distributions. However, the method of variance estimates recovery and normal approximation approaches are alternative competitors for constructing simultaneous confidence intervals, especially when the populations have large variance. We also include two practical applications demonstrating the use of the techniques on observed data, where one data set works for the PM2.5 mass concentrations in Bangkapi and Dindaeng in Thailand and the other data came from the study of nitrogen-bound bovine serum albumin produced by three groups of diabetic mice. Both applications show that the confidence intervals from the parametric bootstrap approach have the smallest length. [ABSTRACT FROM AUTHOR]

The classic credit risk structured model assumes that risky asset values obey geometric Brownian motion. In reality, however, risky asset values are often not a continuous and symmetrical process, but rather they appear to jump and have asymmetric characteristics, such as higher peaks and fat tails. On the other hand, there are real Knight uncertainty risks in financial markets that cannot be measured by a single probability measure. This work examined a structural credit risk model in the Lévy market under Knight uncertainty. Using the Lévy–Laplace exponent, we established dynamic pricing models and obtained intervals of prices for default probability, stock values, and bond values of enterprise, respectively. In particular, we also proved the explicit solutions for the three value processes above when the jump process is assumed to follow a log-normal distribution. Finally, the important impacts of Knightian uncertainty on the pricing of default probability and stock values of enterprise were studied through numerical analysis. The results showed that the default probability of enterprise, the stock values, and bond values were no longer a certain value, but an interval under Knightian uncertainty. In addition, the interval changed continuously with the increase in Knightian uncertainty. This result better reflected the impact of different market sentiments on the equilibrium value of assets, and expanded decision-making flexibility for investors. [ABSTRACT FROM AUTHOR]

Analysis of longitudinal semicontinuous data characterized by subjects' attrition triggered by nonrandom dropout is complex and requires accounting for the within-subject correlation, and modeling of the dropout process. While methods that address the within-subject correlation and missing data are available, approaches that incorporate the nonrandom dropout, also referred to informative right censoring, in the modeling step are scarce due to the computational intensity and possible intractable integration needed for its implementation. Appreciating the complexity of this problem and the need for a new methodology that is feasible for implementation, we propose to extend a framework of likelihood-based marginalized two-part models to account for informative right censoring. The censoring process is modeled using two approaches: (1) Poisson censoring for the count of visits before dropout and (2) survival time to dropout. Novel consideration was given to the proposed joint modeling approaches for the semicontinuous and censoring components of the likelihood function which included (1) shared parameter, and (2) Clayton copula. The cross-part and within-part correlations were accounted for through a complex random effect structure that models correlated random intercepts and slopes. Feasibility of implementation, and accuracy of these approaches were investigated using extensive simulation studies and clinical application. [ABSTRACT FROM AUTHOR]

The paper considers different confidence intervals for the population coefficient of variation based on the resampling methods, the ranked set sampling, the resampling methods for the ranked set samples and the partial ranked set sampling. We modify the existing confidence intervals for the population coefficient of variation using the trimmed mean in order to get better coverage accuracy. The results for the Gamma, Weibull, Log-normal and skew-normal distributions and for the real data set are reported. The best coverage probabilities are obtained using the confidence intervals based on the trimmed mean. [ABSTRACT FROM AUTHOR]

The identification of an appropriate probability model is always essential in environmental data analysis. This work presents the notion of the neutrosophic lognormal distribution (NLD) and its application to environmental data. The general structure for the density function of the NLD and its usefulness has been provided. Some more critical distributional properties such as moments, skewness and kurtosis coefficients have been derived. A methodology of estimating the distributional parameters under the neutrosophic environment is developed. The simulation study is conducted to validate the derived results for the proposed model. In the application part, a real dataset on Nitrogen oxides emissions has been analyzed using NLD to highlight the practical significance of the proposed model. [ABSTRACT FROM AUTHOR]

'Effective discharge' is defined as a discharge that carries maximum amount of sediments over a prolonged period of time. Magnitude–Frequency Analysis (MFA) provides a mathematical framework to determine effective discharge. MFA considers (1) the discharge at a location that follows a lognormal probability distribution and (2) sediment load which exhibits a power law relationship with the discharge. An important task for hydrologists is to determine reliable estimates of effective discharge at locations of interest within river basins. There is a dearth of attempts to assess effective discharge estimates within South Indian River basins. Present study demonstrates the utility of MFA to arrive at effective discharge estimates based on daily and monthly stream flow data at 30 gauges in four southern river (Mahanadi, Godavari, Krishna and Cauvery) basins flowing through Indian Peninsular region. Evaluation of effective discharge at daily and monthly timescales is carried out to understand the behavior of effective discharge estimates over different timescales. It was observed that the assumption of lognormality was invalid for daily discharge data at all gauges while it was valid at monthly scale for 12 gauges. Results from this study can find use in efficacious planning and management of reservoirs in South India. [ABSTRACT FROM AUTHOR]

Existing models of human body surface communication channels only consider the single frequency or UWB ( ultra wide band ) frequency band, and the research objects are static human body model. This paper established 35 human body models in continuous postures based on FDTD (finite difference time domain ) method and analyzed the transmission characteristics of dynamic HBC( human body communication ) channel. It confirmed that path loss was directly proportional to the communication distance . This paper analyzed the multipath effect of dynamic human body channel by using the modified S-V model, and verified this model. Finally, this paper determined that the cumulative probability density of the average power gain conformed to the lognormal distribution according to the second-order information criterion. By comparing this result with that of UWB band, body motions in HBC frequency band had less influence on body communication transmission characteristics. Therefore, the HBC frequency band is more suitable to body surface communication. [ABSTRACT FROM AUTHOR]

The lognormal distribution is commonly used to characterize the aleatory variability of ground-motion prediction equations (GMPEs) in probabilistic seismic hazard analysis (PSHA). However, this approach often leads to results without actual physical meaning at low exceedance probabilities. In this paper, we discuss how to calculate PSHA with a low exceedance probability. Peak ground acceleration records from the NGA-West2 database and 15,493 residuals calculated by Campbell-Bozorgnia using the NGA-West2 GMPE were applied to analyze the tail shape of the residuals. The results showed that the generalized Pareto distribution (GPD) captured the characteristics of residuals in the tail better than the lognormal distribution. Further study showed that the shapes of the tails of the distributions of residuals with different magnitudes varied significantly due to the heteroscedasticity of the magnitude; the distribution of residuals with larger magnitudes had a smaller upper limit on the right side. Moreover, the residuals of the three magnitude ranges given in this study were more consistent with the GPD of different parameters at the tail than the lognormal distribution and the GPD fitted by all the residuals, leading to a bounded PSHA hazard curve. Therefore, the lognormal distribution is more representative up to a determined threshold, and the GPD fitted to the residuals of three ranges of magnitude better characterizes the tail for PSHA calculation. [ABSTRACT FROM AUTHOR]

Objectives: Survival extrapolation of trial outcomes is required for health economic evaluation. Generally, all-cause mortality (ACM) is modeled using standard parametric distributions, often without distinguishing disease-specific/excess mortality and general population background mortality (GPM). Recent National Institute for Health and Care Excellence guidance (Technical Support Document 21) recommends adding GPM hazards to disease-specific/excess mortality hazards in the log-likelihood function ("internal additive hazards"). This article compares alternative extrapolation approaches with and without GPM adjustment.Methods: Survival extrapolations using the internal additive hazards approach (1) are compared to no GPM adjustment (2), applying GPM hazards once ACM hazards drop below GPM hazards (3), adding GPM hazards to ACM hazards (4), and proportional hazards for ACM versus GPM hazards (5). The fit, face validity, mean predicted life-years, and corresponding uncertainty measures are assessed for the active versus control arms of immature and mature (30- and 75-month follow-up) multiple myeloma data and mature (64-month follow-up) breast cancer data.Results: The 5 approaches yielded considerably different outcomes. Incremental mean predicted life-years vary most in the immature multiple myeloma data set. The lognormal distribution (best statistical fit for approaches 1-4) produces survival increments of 3.5 (95% credible interval: 1.4-5.3), 8.5 (3.1-13.0), 3.5 (1.3-5.4), 2.9 (1.1-4.5), and 1.6 (0.4-2.8) years for approaches 1 to 5, respectively. Approach 1 had the highest face validity for all data sets. Uncertainty over parametric distributions was comparable for GPM-adjusted approaches 1, 3, and 4, and much larger for approach 2.Conclusion: This study highlights the importance of GPM adjustment, and particularly of incorporating GPM hazards in the log-likelihood function of standard parametric distributions. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Harbin Institute of Technology. Social Sciences Edition / Haerbin Gongye Daxue Xuebao. Shehui Kexue Ban is the property of Harbin Institute of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Suppose that a policyholder faces n risks X1;: ::;Xn which are insured under the policy limit with the total limit of l. Usually, the policyholder is asked to protect each Xi with an arbitrary limit of li such that Pni =1 li = l. If the risks are independent and identically distributed with log-concave cumulative distribution function, using the notions of majorization and stochastic orderings, we prove that the equal limits provide the maximum of the expected utility of the wealth of policyholder. If the risks with log-concave distribution functions are independent and ordered in the sense of the reversed hazard rate order, we show that the equal limits is the most favourable allocation among the worst allocations. We also prove that if the joint probability density function is arrangement increasing, then the best arranged allocation maximizes the utility expectation of policyholder's wealth. We apply the main results to the case when the risks are distributed according to a log-normal distribution. [ABSTRACT FROM AUTHOR]

We propose a method for estimating the nonlinear functional of the probability density of a two-dimensional random variable. The technique applies to the implementation of procedures for the "quick" selection of blur coefficients in the problem of optimizing kernel estimates of the probability density and can significantly increase the computational efficiency of nonparametric decision rules. The proposed approach is based on the analysis of the formula for the optimal blur coefficient of the kernel probability density estimate. In this case, the kernel function blur coefficient is presented as a product of an indefinite parameter and standard deviations of random variables. The main component of the indefinite parameter is a nonlinear functional of the probability density, which for a family of unimodal symmetric distribution laws is determined by the form of the probability density and does not depend on the density parameters of. For a family of two-dimensional lognormal distribution laws of independent random variables, we determine the approximation errors of the considered nonlinear functional of the probability density. We study the possibility of using the proposed methodology for estimating nonlinear functionals on probability densities that differ from lognormal distribution laws. We analyze the influence of the occurring approximation errors on the RMS criteria for reconstructing the nonparametric estimate of the probability density of a two-dimensional random variable. [ABSTRACT FROM AUTHOR]

This contribution addresses the estimation of exceedance probabilities of the dynamic random response of railway bridges subjected to high-speed trains in the presence of random rail irregularities. The random nature of the irregular rail track is described by a spatial ergodic stochastic process, and consequently the dynamic bridge response becomes a stochastic process in time with generally unknown distributions. Using numerical simulation methods, the response thresholds for bridge deflection and acceleration are estimated to obtain small exceedance probabilities. Combining these limits with the response at perfect rail geometry provides an estimate of the dynamic response amplification due to random rail irregularities. This is in line with the semi-probabilistic safety concept of modern civil engineering, where critical response thresholds for structures are associated with small exceedance probabilities. It is shown that modeling the maximum bridge deflection as a normally distributed random variable with parameters fitted to the results of a Monte Carlo simulation with small sample size is a computationally efficient approach for estimating the amplified deflection. In contrast, the random maximum bridge acceleration is better captured by a lognormal distribution. As an efficient alternative, the subset simulation method provides accurate predictions for very small exceedance probabilities. If the amplitudes of the rail irregularities at discrete spatial coordinates along the rail axis are considered as random variables, the stability of subset simulation increases. [ABSTRACT FROM AUTHOR]

At‐site flood frequency analysis is a direct method of flood estimation at a given site. The choice of an appropriate probability distribution and parameter estimation method plays a vital role in at‐site frequency analysis. In the current article, flood frequency analysis is carried out at five gauging sites of the Ume River in Sweden. Generalised extreme value, three‐parameter log‐normal, generalised logistic and Gumbel distributions are fitted to the annual maximum peak flow data. The L‐moment and the maximum likelihood methods are used to estimate the parameters of the distributions. Based on different goodness‐of‐fit tests and accuracy measures, the three‐parameter log‐normal distribution has been identified as the best‐fitted distribution by using the L‐moments method of estimation for gauging sites Harrsele Krv, Gardiken and Överuman Nedre. The generalised extreme value distribution with the L‐moments estimation provided the best fit to maximum annual streamflow at gauging sites Solberg and Stornorrfors Krv. Finally, the best‐fitted distribution for each gauging site is used to predict the maximum flow of water for return periods of 5, 10, 25, 50, 100, 200, 500, and 1000 years. [ABSTRACT FROM AUTHOR]

In this article, we describe a quantitative approach for comparing the reliability or survival functions for two populations. The Bayesian probability of agreement (BPA) quantifies the similarity of the functions in regions of interest in the covariate space while accounting for a user-specified measure of what constitutes a practically important difference. The BPA method can be flexibly used for relationships with any number of covariates and for a variety of parametric models, including Weibull, lognormal and gamma regression. We provide an R Shiny app that allows practitioners to easily use the method without the need to implement the underlying computational details. Three examples from industrial and medical applications illustrate the implementation of the method as well as how to interpret the results from the analysis. [ABSTRACT FROM AUTHOR]

State actors can minimize the risk of combat deaths by making decisions consistent with a likelihood ratio test that fuses attack detection data with prior war probabilities. The power-law, which has for decades been used to model the distribution of combat fatalities, is invalid as a probability because the mean is divergent. An investigation of Correlates of War data reveal that combat fatalities follow a log-gamma or log-normal probability distribution depending if a state's strategy is offensive or defensive. This finding is linked to a state actor model where combat deaths have logarithmic utility and defensive strategies appear lower risk than offensive strategies. Results suggests that minimum-risk decision thresholds be derived from defensive statistics. The method of computing the thresholds is illustrated using war statistics from NATO countries. [ABSTRACT FROM AUTHOR]

The divergence between the Pareto distribution and the log-normal distribution has been observed persistently over the past couple of decades in complex network research, economics, and social sciences. To address this, we here propose an approach termed as the accumulative law and its related probability model. We show that the resulting accumulative distribution has properties that are akin to both the Pareto distribution and the log-normal distribution, which leads to a broad range of applications in modelling and fitting real data. We present all the details of the accumulative law, describe the properties of the distribution, as well as the allocation and the accumulation of variables. We also show how the proposed accumulative law can be applied to generate complex networks, to describe the accumulation of personal wealth, and to explain the scaling of internet traffic across different domains. [ABSTRACT FROM AUTHOR]

In this paper, we develop a matching prior for the common mean in several log-normal distributions. For this problem, assigning priors appropriately for the common log-normal mean is challenging owing to the presence of nuisance parameters. Matching priors, which are priors that match the posterior probabilities of certain regions within their frequentist coverage probabilities, are commonly used in this problem. However, a closed form posterior under the derived first order matching prior is not available; further, the second order matching prior is difficult to be derived in this problem. Thus, alternatively, we derive a matching prior based on a modification of the profile likelihood. Simulation studies show that this proposed prior meets the target coverage probabilities very well even for small sample sizes. Finally, we present a real example. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Harbin Institute of Technology. Social Sciences Edition / Haerbin Gongye Daxue Xuebao. Shehui Kexue Ban is the property of Harbin Institute of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

• Uncertainty analysis should incorporate state-of-knowledge correlation (SOKC). • SOKC effects on lognormal, beta, and gamma distributions are explored. • Mathematical proofs for the heightened SOKC impact in lognormal over gamma or beta. • Illustration with frequency calculation of interfacing system coolant loss accidents. • The mathematical proofs bear significance for probability and statistics theories. In the probabilistic safety assessment (PSA) of nuclear power plants, the state-of-knowledge correlation (SOKC) is required to be considered when estimating the risk measures and their uncertainties. Specifically, the SOKC must be taken into account when the failure data for similar components are aggregated to produce the failure rate or failure probability for the components and their uncertainty distributions. The objective of this study is to mathematically prove what has been numerically observed in the existing studies: The SOKC effect is more significant if the uncertainty is modeled with a lognormal distribution than when it is modeled with a gamma or beta distribution when the parameters of the two distributions are estimated from the same failure data by using the method of moments. An example based on the frequency calculation for interfacing system loss of coolant accidents is provided to demonstrate the proof. The mathematical proof provides a relationship between the raw moments of lognormal, gamma, and beta distributions, which is expected to be valuable in probability and statistics theories. [ABSTRACT FROM AUTHOR]

Introduction: Quality indicators (QI) based on percentiles are widely used for managing quality in laboratory medicine nowadays. Due to their statistical nature, their estimation is affected by sampling so they should be always presented together with the confidence interval (CI). Since no methodological recommendation has been issued to date, our aim was investigating the suitability of the parametric method (LP-CI), the non-parametric binomial (NP-CI) and bootstrap (BCa-CI) procedures for the CI estimation of 2.5th, 25th, 50th, 75th and 97.5th percentile in skewed sets of data. Materials and methods: Skewness was reproduced by numeric simulation of a lognormal distribution in order to have samples with different right-tailing (moderate, heavy and very heavy) and size (20, 60 and 120). Performance was assessed with respect to the actual coverage probability (ACP, accuracy) against the confidence level of 1-α with α = 0.5, and the median interval length (MIL, precision). Results: The parametric method was accurate for sample size N ≥ 20 whereas both NP-CI and BCa-CI required N ≥ 60. However, for extreme percentiles of heavily right-tailed data, the required sample size increased to 60 and 120 units respectively. A case study also demonstrated the possibility to estimate the ACP from a single sample of real-life laboratory data. Conclusions: No method should be applied blindly to the estimation of CI, especially in small-sized and skewed samples. To this end, the accuracy of the method should be investigated through a numeric simulation that reproduces the same conditions of the real-life sample. [ABSTRACT FROM AUTHOR]

Outage probability analysis of diversity reception over lognormal fading channels is challenging because the cumulative distribution function (CDF) of a sum of lognormal random variables (RVs) does not yield a closed-form expression. Furthermore, traditional asymptotic analysis techniques fail for lognormal fading channels. The well-applied approximation techniques, such as Fenton, Wilkinson, and Schwartz and Yeh approximations, become unreliable when the signal-to-noise ratio (SNR) is high. In this paper, we derive closed-form bounds of outage probability for dual-branch equal-gain combining system over non-identically distributed lognormal fading channels. The bounds are shown tight from low-to-high SNR regimes, which provides an efficient way to evaluate the EGC system without resorting to expensive Monte Carlo simulation or numerical integration. Furthermore, the new analytical expressions can be used to test at what SNR the existing approximation techniques become inaccurate, and can also be used as criteria for system design. [ABSTRACT FROM AUTHOR]

In wireless communication channels, the signals arriving at the receiver may be of stochastic nature or be superpositioned due to non-uniform scattering and shadowing. For the ease of computation, we generally assume the mean ergodic property of communication channels which is error prone. The well known lognormal model fails to capture the extreme tail fluctuations in the presence of shadowing. In this setting, we exploit the importance of Tsallis non-extensive parameter 'q' to characterize various fading channels. The q-lognormal distribution captures the tail phenomena due to presence of non-extensive parameter 'q'. In this paper, we provide an excellent agreement between the generated synthetic signal and the proposed q-Lognormal distribution for different values of parameter 'q'. This paper also presents the analytical expression for the superstatistics Weibull/q-lognormal model to capture both fading and shadowing effects. It is observed that the Weibull/q-Lognormal model provides a better fit to the generated signal for q = 1.8 in comparison to the well known Weibull/Lognormal model. Finally, we provide an excellent agreement between the derived measures viz., amount of fading, outage probability, average channel capacity with extensive Monte-Carlo simulation scheme. [ABSTRACT FROM AUTHOR]

Arithmetic Asian options are difficult to price and hedge as they do not have closed-form analytic solutions. The main theoretical reason for this difficulty is that the payoff depends on the finite sum of correlated lognormal variables, which is not lognormal and for which there is no recognizable probability density function. We use elementary techniques to derive the probability density function of the infinite sum of correlated lognormal random variables and show that it is reciprocal gamma distributed, under suitable parameter restrictions. A random variable is reciprocal gamma distributed if its inverse is gamma distributed. We use this result to approximate the finite sum of correlated lognormal variables and then value arithmetic Asian options using the reciprocal gamma distribution as the state-price density function. We thus obtain a closed-form analytic expression for the value of an arithmetic Asian option, where the cumulative density function of the gamma distribution, G(d) in our formula, plays the exact same role as N(d) in the Black-Scholes/Merton formula. In addition to being theoretically justified and exact in the limit, we compare our method against other algorithms in the literature and show our method is quicker, at least as accurate, and, in our opinion, more intuitive and pedagogically appealing than any previously published result, especially when applied to high yielding currency options. [ABSTRACT FROM AUTHOR]

Highlights • The JIF is used as a surrogate of the citation for paper evaluation. • We compare the evaluations of two papers by the JIF and the number of citations. • JIF paper evaluation fails when the JIF evaluation contradicts citation evaluation. • We find high failure probabilities in JIF evaluations, as high as 0.5 in many cases. Abstract The journal impact factor (JIF) is the average of the number of citations of the papers published in a journal, calculated according to a specific formula; it is extensively used for the evaluation of research and researchers. The method assumes that all papers in a journal have the same scientific merit, which is measured by the JIF of the publishing journal. This implies that the number of citations measures scientific merits but the JIF does not evaluate each individual paper by its own number of citations. Therefore, in the comparative evaluation of two papers, the use of the JIF implies a risk of failure, which occurs when a paper in the journal with the lower JIF is compared to another with fewer citations in the journal with the higher JIF. To quantify this risk of failure, this study calculates the failure probabilities, taking advantage of the lognormal distribution of citations. In two journals whose JIFs are ten-fold different, the failure probability is low. However, in most cases when two papers are compared, the JIFs of the journals are not so different. Then, the failure probability can be close to 0.5, which is equivalent to evaluating by coin flipping. [ABSTRACT FROM AUTHOR]

The increase in the cover depth and length of longwall face leads to some drastic changes in mine pressure occurrence and spatial distribution. Such changes result in a great challenge in surrounding rock control. In order to realize an effective control of the abnormal mine pressure occurrences, happening frequently and difficult to be predicted in deep longwall face with ultra-large length,the roof rupture characteristics and support resistance distribution in such a longwall face are investigated. Pre-existing fracture development significantly increases due to the increase of cover depth. The fracture size and orientations obey lognormal and normal distributions, respectively. The main roof with randomly distributed fractures is reconstructed based on such statistical distributions and DFN method. The large length of longwall face increases the probability of the existence of fractures in exposed main roof. Sub-regional rupture model is established for the main roof with one and two fractures, whose limit load-bearing capacities are achieved. The mechanical condition for the occurrence of the sub-regional rupture of main roof and its subsequent migration is achieved using upper bound theory. Spatial distribution of the broken blocks after the main roof fracturing is non-uniform. The block volume in the middle section of the longwall face is small while that of the blocks on two sides of the longwall face is relatively large. Such distribution reasonably explains the non-uniform distribution of the support resistance along the dip direction of the longwall face. The theoretical conclusions are in good accordance with the experimental results and field measurement. [ABSTRACT FROM AUTHOR]

Purpose: Motor vehicle crashes are one of the leading causes of traumatic brain injuries. Restraint systems of cars are evaluated by crash tests based on human tolerance data, however, the reliability of data currently used has been questioned several times in the literature due to the neglect of certain types of effects, injury types and uncertainties. Our main goal was to re-evaluate the currently applied risk curve by taking the previously neglected effects into account. Methods: In this paper, the probability of traumatic brain injury was determined by reliability analysis where different types of uncertainties are taken into account. The tissue-level response of the human brain in the case of frontal crashes was calculated by finite element analyses and the injury probability is determined by Monte Carlo simulations. Sensitivity analysis was also performed to identify which effects have considerable contribution to the injury risk. Results: Our results indicate a significantly larger injury risk than it is predicted by current safety standards. Accordingly, a new risk curve was constructed which follows a lognormal distribution with the following parameters: μLN = 6.5445 and σLN = 1.1993. Sensitivity analysis confirmed that this difference primarily can be attributed to the rotational effects and tissue-level uncertainties. Conclusions: Results of the tissue-level reliability analysis enhance the belief that rotational effects are the primary cause of brain injuries. Accordingly, the use of a solely translational acceleration based injury metric contains several uncertainties which can lead to relatively high injury probabilities even if relatively small translational effects occur. [ABSTRACT FROM AUTHOR]

As a function of fragility curves in earthquake engineering, the assessment of the probability of exceeding a specific damage state according to the magnitude of earthquake can be considered. Considering that the damage states for fragility curves are generally nested to each other, the possibility theory, a special form of the evidence theory for nested intervals, is applied to generate fragility information from seismic damage data. While the lognormal distributions are conventionally used to generate fragility curves due to their simplicity and applicability, the methodology to use the possibility theory does not require the assumption of distributions. Seismic damage data classified by four damage levels were used for a case study. The resulted possibility-based fragility information expressed by two monotone measures, "possibility" and "certainty," are compared with the conventional fragility curves based on probability. The results showed that the conventional fragility curves provide a conservative estimation at the relatively high earthquake magnitude compared with the possibility-based fragility information. [ABSTRACT FROM AUTHOR]

This paper presents the development of a simplified model for estimation of maximum nail loads during or at completion of construction of soil nail walls. The developed simplified nail load model consists of two multiplicative components: the theoretical nail load and the correction factor. The theoretical nail load is computed as the product of lateral active Earth pressure at nail depth and the nail tributary area. The correction factor is introduced to account for the difference between the theoretical and the measured nail loads. A total of 85 measured nail load data were collected from the literature; out of which, 74 were used to develop a simple formulation for the correction factor, whereas the remaining 11 were used for validation. After the validation, the model was updated using all 85 data. The updated simplified nail load model was demonstrated to be accurate on average (mean of model factor equal to 1), and the spread in prediction quantified as the coefficient of variation of the model factor was about 40%. Here, model factor is the ratio of measured to estimated nail load. The randomness of the model factor was also verified. Finally, the model factor was demonstrated to be a lognormal random variable. The proposed simplified nail load model is beneficial due to its simplicity and quantified model uncertainty; thus it is practically valuable to both direct reliability-based design and load and resistance factor design of soil nail wall internal limit states. [ABSTRACT FROM AUTHOR]

Birnbaum-Saunders fatigue life distribution is an important failure model in the probability physical methods. It is more suitable for describing the life rules of fatigue failure products than common life distributions such as Weibull distribution and lognormal distribution. Besides, it is mainly applied to analytical research about fatigue failure and degradation failure of electronic product performance. The characteristic properties such as numerical characteristics and image features of density function and failure rate function are studied for generalized BS fatigue life distribution GBS(α, β,m) in this paper. Then the point estimates and approximate interval estimates of parameters are proposed for generalized BS fatigue life distribution GBS(α, β,m), and the precision of estimates are investigated by Monte Carlo simulations. Finally, when the scale parameter satisfies inverse power law model, the failure distribution model is given for the products of two-parameter BS fatigue life distribution BS(α, β) under progressive stress accelerated life test according to the time conversion idea of famous Nelson assumption, and then the points estimates of parameters are given. [ABSTRACT FROM AUTHOR]

Abstract: Fault trees are used in reliability modeling to create logical models of fault combinations that can lead to undesirable events. The output of a fault tree analysis (the top event probability) is expressed in terms of the failure probabilities of basic events that are input to the model. Typically, the basic event probabilities are not known exactly, but are modeled as probability distributions: therefore, the top event probability is also represented as an uncertainty distribution. Monte Carlo methods are generally used for evaluating the uncertainty distribution, but such calculations are computationally intensive and do not readily reveal the dominant contributors to the uncertainty. In this article, a closed‐form approximation for the fault tree top event uncertainty distribution is developed, which is applicable when the uncertainties in the basic events of the model are lognormally distributed. The results of the approximate method are compared with results from two sampling‐based methods: namely, the Monte Carlo method and the Wilks method based on order statistics. It is shown that the closed‐form expression can provide a reasonable approximation to results obtained by Monte Carlo sampling, without incurring the computational expense. The Wilks method is found to be a useful means of providing an upper bound for the percentiles of the uncertainty distribution while being computationally inexpensive compared with full Monte Carlo sampling. The lognormal approximation method and Wilks’s method appear attractive, practical alternatives for the evaluation of uncertainty in the output of fault trees and similar multilinear models. [ABSTRACT FROM AUTHOR]

Seismic vulnerability assessment helps to estimate the extent and the probability of damage to buildings due to the potential earthquake hazard. Determination of structural fragility curves of buildings is one of the most important steps in seismic vulnerability assessment. The fragility curve predicts the probability of exceeding specific damage states for a seismic intensity parameter. This paper is focused on the development of structural fragility curves for different building types in the Sarpol-e Zahab city. For this purpose, a reconnaissance survey was conducted after the Sarpol-e Zahab earthquake of November 12, 2017 to identify the damage state of various buildings based on the HAZUS Methodology. Then, the improveddisplacement coefficient method implemented in the SELENA software was used for expressing building loss probabilities. In order to find out which level of the seismic design can be used in defining the fragility curves, different weights were considered to apply to the HAZUS fragility curves of high, moderate, low and pre-code to be used in the logic tree method. Finally, the mean and standard deviation values were introduced for the construction of fragility curves with the lognormal distribution for the seven Iranian building types. [ABSTRACT FROM AUTHOR]

Lee and Krutchkoff [Biometrics, 36, 1980, 531-536] introduced partially truncated distributions and derived their mean and variance with applications to a contaminant data set. Here, we derive the moments of partially truncated distributions of general order. We revisit the data application of Lee and Krutchkoff to show that the conclusion can be different for different orders. [ABSTRACT FROM AUTHOR]

• The strength probability density distribution of CFRP plate exhibit double peaks characteristic, indicating that the dominant defects in CFRP plates may be not single, but include fiber defects and pultrusion process defects. • The proposed Couple-Weibull distribution is capable to accurately describe the probabilistic characteristic for tensile strength of CFPR plates by adjusting the weight parameters, shape parameters and position parameters. • The length effect has nonneglectable influence on the tensile strength of CFPR plates, and the tensile strength of CFPR plate with length of 100 m is about 17% lower than that with length of 150 mm. • A revised coefficient for characteristic stress in Couple-Weibull model is suggested to consider length effect, which varies little when the length of CFRP plate exceeds 20 m. • The length effect is relatively obvious within 2000 mm, and gradually become littler with the length increasing to 100 m. After the length exceeds 100 m, the length effect becomes quite slight. This manuscript investigates the probability model and the length effect of tensile strength for unidirectional plates of carbon fiber reinforced polymers (CFRP). Firstly, 30 unidirectional CFRP plates with length of 250 mm are investigated by tensile strength tests and statistical analysis of strength probability characteristics with Normal, Lognormal, traditional Weibull and couple-Weibull distribution. While the test results show that the probability density curve of tensile strength exhibits double peaks, a couple-Weibull model is proposed to describe the probability characteristics of tensile strength, which exhibits good accuracy and applicability with comparison to the experimental results. On this basis, the tensile strength of ten groups of unidirectional CFRP plates with different lengths is tested. The results show that the influence of length effect on tensile strength is significant, and the maximum strength reduction rate is 17.11%. Finally, a probability model of tensile strength considering length effect is established based on couple-Weibull model. With comparison to the test results, it is validated to properly consider the variation of tensile strength with different lengths for unidirectional CFRP plate and give accurate prediction results. [ABSTRACT FROM AUTHOR]

The incubation period for typhoid, polio, measles, leukemia and many other diseases follows a right-skewed, approximately lognormal distribution. Although this pattern was discovered more than sixty years ago, it remains an open question to explain its ubiquity. Here, we propose an explanation based on evolutionary dynamics on graphs. For simple models of a mutant or pathogen invading a network-structured population of healthy cells, we show that skewed distributions of incubation periods emerge for a wide range of assumptions about invader fitness, competition dynamics, and network structure. The skewness stems from stochastic mechanisms associated with two classic problems in probability theory: the coupon collector and the random walk. Unlike previous explanations that rely crucially on heterogeneity, our results hold even for homogeneous populations. Thus, we predict that two equally healthy individuals subjected to equal doses of equally pathogenic agents may, by chance alone, show remarkably different time courses of disease. [ABSTRACT FROM AUTHOR]

Standardized likelihood ratio test (SLRT) for testing the equality of means of several log-normal distributions is proposed. The properties of the SLRT and an available modified likelihood ratio test (MLRT) and a generalized variable (GV) test are evaluated by Monte Carlo simulation and compared. Evaluation studies indicate that the SLRT is accurate even for small samples, whereas the MLRT could be quite liberal for some parameter values, and the GV test is in general conservative and less powerful than the SLRT. Furthermore, a closed-form approximate confidence interval for the common mean of several log-normal distributions is developed using the method of variance estimate recovery, and compared with the generalized confidence interval with respect to coverage probabilities and precision. Simulation studies indicate that the proposed confidence interval is accurate and better than the generalized confidence interval in terms of coverage probabilities. The methods are illustrated using two examples. [ABSTRACT FROM AUTHOR]