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AbstractAccurate model performance assessment in survival analysis is imperative for robust predictions and informed decision-making. Traditional residual diagnostic tools like martingale and deviance residuals lack a well-characterized reference distribution for censored regression, making numerical statistical tests based on these residuals challenging. Recently, the introduction of Z-residuals for diagnosing survival models addresses this limitation. However, concerns arise from conventional methods that utilize the entire dataset for both model parameter estimation and residual assessment, which may cause optimistic biases. This paper introduces cross-validatory Z-residuals as an innovative approach to address these limitations. Employing a cross-validation (CV) framework, the method systematically partitions the dataset into training and testing sets to reduce the optimistic bias. Our simulation studies demonstrate that, for goodness-of-fit tests and outlier detection, cross-validatory Z-residuals are significantly more powerful (e.g. power increased from 0.2 to 0.6). and more discriminative (e.g. AUC increased from 0.58 to 0.85) than Z-residuals without CV. We also compare the performance of Z-residuals with and without CV in identifying outliers in a real application that models the recurrence time of kidney infection patients. Our findings suggest that cross-validatory Z-residuals can identify outliers, which Z-residuals without CV fail to identify. The CV Z-residual is a more powerful tool than the No-CV Z-residual for checking survival models, particularly in goodness-of-fit tests and outlier detection. We have published a generic function, which is collected in an R package called Zresidual, for computing CV Z-residual for the output of the widely used survival R package. [ABSTRACT FROM AUTHOR]

We introduce a generalized version of a unit distribution called power unit exponential probability distribution (PUEPrD) using the power transformation of the unit exponential probability distribution. Some statistical properties of the proposed distribution are derived. For some selected parameter cases, we have demonstrated that the hazard function of the proposed distribution can be shaped by increasing and bathtub curves. Twelve estimation methods such as maximum likelihood, Anderson–Darling, Cramer–von-Mises, maximum product spacings, least squares, weighted least squares, right tail Anderson Darling, left-tail Anderson Darling, minimum spacing absolute distance, minimum spacing absolute-log distance, Anderson Darling left-tail second order, Kolmogorov are used to estimate the parameters of the suggested distribution. A numerical simulation study is conducted to check the efficiency of the parameter estimates of the proposed model. With the help of some real-life data sets, the flexibility and usefulness of the PUEPrD are illustrated. As a result of two real data analyses, we observe that the fit of the proposed distribution to the data is superior to its competitors according to the examined criteria.

Abstract Background Synthetic Electronic Health Records (EHRs) are becoming increasingly popular as a privacy enhancing technology. However, for longitudinal EHRs specifically, little research has been done into how to properly evaluate synthetically generated samples. In this article, we provide a discussion on existing methods and recommendations when evaluating the quality of synthetic longitudinal EHRs. Methods We recommend to assess synthetic EHR quality through similarity to real EHRs in low-dimensional projections, accuracy of a classifier discriminating synthetic from real samples, performance of synthetic versus real trained algorithms in clinical tasks, and privacy risk through risk of attribute inference. For each metric we discuss strengths and weaknesses, next to showing how it can be applied on a longitudinal dataset. Results To support the discussion on evaluation metrics, we apply discussed metrics on a dataset of synthetic EHRs generated from the Medical Information Mart for Intensive Care-IV (MIMIC-IV) repository. Conclusions The discussion on evaluation metrics provide guidance for researchers on how to use and interpret different metrics when evaluating the quality of synthetic longitudinal EHRs.

Background: Synthetic Electronic Health Records (EHRs) are becoming increasingly popular as a privacy enhancing technology. However, for longitudinal EHRs specifically, little research has been done into how to properly evaluate synthetically generated samples. In this article, we provide a discussion on existing methods and recommendations when evaluating the quality of synthetic longitudinal EHRs. Methods: We recommend to assess synthetic EHR quality through similarity to real EHRs in low-dimensional projections, accuracy of a classifier discriminating synthetic from real samples, performance of synthetic versus real trained algorithms in clinical tasks, and privacy risk through risk of attribute inference. For each metric we discuss strengths and weaknesses, next to showing how it can be applied on a longitudinal dataset. Results: To support the discussion on evaluation metrics, we apply discussed metrics on a dataset of synthetic EHRs generated from the Medical Information Mart for Intensive Care-IV (MIMIC-IV) repository. Conclusions: The discussion on evaluation metrics provide guidance for researchers on how to use and interpret different metrics when evaluating the quality of synthetic longitudinal EHRs. [ABSTRACT FROM AUTHOR]

Gamma processes are commonly used for modelling the accumulative deterioration of systems, in many fields. However, given a series of observations, it is not always easy to affirm that the choice of a gamma process modelling is a good choice. In particular, it would be of great interest to have a statistical test, i.e. a goodness-of-fit test, to answer this question. In this paper, a practical procedure combining three statistical tests is firstly proposed, whose aim is to reject the gamma process modelling as soon as the observations are clearly in contradiction with the basic properties of a homogeneous gamma process, observed with periodic inspections: stationarity, independence and gamma distribution for the increments. The procedure is then extended to non-homogeneous gamma process and aperiodic inspection times. The efficiency of the approach is investigated through numerical simulations, and on real data. [ABSTRACT FROM AUTHOR]

Introduction: Cross frequency coupling (CFC) between electrophysiological signals in the brain is a long-studied phenomenon and its abnormalities have been observed in conditions such as Parkinson's disease and epilepsy. More recently, CFC has been observed in stomach-brain electrophysiologic studies and thus becomes an enticing possible target for diseases involving aberrations of the gut-brain axis. However, current methods of detecting coupling, specifically phase-amplitude coupling (PAC), do not attempt to capture the phase and amplitude statistical relationships. Methods: In this paper, we first demonstrate a method of modeling these joint statistics with a flexible parametric approach, where we model the conditional distribution of amplitude given phase using a gamma distributed generalized linear model (GLM) with a Fourier basis of regressors. We perform model selection with minimum description length (MDL) principle, demonstrate a method for assessing goodness-of-fit (GOF), and showcase the efficacy of this approach in multiple electroencephalography (EEG) datasets. Secondly, we showcase how we can utilize the mutual information, which operates on the joint distribution, as a canonical measure of coupling, as it is non-zero and non-negative if and only if the phase and amplitude are not statistically independent. In addition, we build off of previous work by Martinez-Cancino et al., and Voytek et al., and show that the information density, evaluated using our method along the given sample path, is a promising measure of time-resolved PAC. Results: Using synthetically generated gut-brain coupled signals, we demonstrate that our method outperforms the existing gold-standard methods for detectable low-levels of phase-amplitude coupling through receiver operating characteristic (ROC) curve analysis. To validate our method, we test on invasive EEG recordings by generating comodulograms, and compare our method to the gold standard PAC measure, Modulation Index, demonstrating comparable performance in exploratory analysis. Furthermore, to showcase its use in joint gut-brain electrophysiology data, we generate topoplots of simultaneous high-density EEG and electrgastrography recordings and reproduce seminal work by Richter et al. that demonstrated the existence of gut-brain PAC. Using simulated data, we validate our method for different types of time-varying coupling and then demonstrate its performance to track time-varying PAC in sleep spindle EEG and mismatch negativity (MMN) datasets. Conclusions: Our new measure of PAC using Gamma GLMs and mutual information demonstrates a promising new way to compute PAC values using the full joint distribution on amplitude and phase. Our measure outperforms the most common existing measures of PAC, and show promising results in identifying time varying PAC in electrophysiological datasets. In addition, we provide for using our method with multiple comparisons and show that our measure potentially has more statistical power in electrophysiologic recordings using simultaneous gut-brain datasets. [ABSTRACT FROM AUTHOR]

In this study, we introduce the modified Burr III Odds Ratio–G distribution, a novel statistical model that integrates the odds ratio concept with the foundational Burr III distribution. The spotlight of our investigation is cast on a key subclass within this innovative framework, designated as the Burr III Scaled Inverse Odds Ratio–G (B-SIOR-G) distribution. By effectively integrating the odds ratio with the Burr III distribution, this model enhances both flexibility and predictive accuracy. We delve into a thorough exploration of this distribution family's mathematical and statistical properties, spanning hazard rate functions, quantile functions, moments, and additional features. Through rigorous simulation, we affirm the robustness of the B-SIOR-G model. The flexibility and practicality of the B-SIOR-G model are demonstrated through its application to four datasets, highlighting its enhanced efficacy over several well-established distributions. [ABSTRACT FROM AUTHOR]

Simulating the probability of type I error is a powerful statistical tool that allows confirming if the statistical test achieves the established nominal level. However, its computational implementation has the drawback of significantly long execution times. Therefore, this article analyzes the performance of two parallel implementations (parRapply and boot) which significantly reduce the execution time of simulations of type I error probability for a goodness-of-fit test for the bivariate Poisson distribution. The results obtained demonstrate how the parallelization strategies accelerate the simulations, reducing the time by 50% to 90% when using 2 to 12 processors running in parallel. This reduction is graphically evidenced as the execution time of the analyzed parallel versions fits almost perfectly ( R 2 ≈ 0.999 ) to the power model y = a p b , where p is the number of processors used, and a > 0 and b < 0 are the constants of the model. Furthermore, it is shown that the parallelization strategies used scale with an increasing number of processors. All algorithms were implemented in the R programming language, and their code is included at the end of this article. [ABSTRACT FROM AUTHOR]

Pinus occidentalis (Swartz) is the primary timber species in the Dominican Republic (DR). Despite its economic importance, studies conducted on this species are scarce, making it difficult to estimate current inventory levels. This study aims to enhance the accuracy of estimating the total bole volume of P. occidentalis in different ecological zones (EZs) within La Sierra, evaluating and comparing two established volume equations—combined variable (CV) and Schumacher and Hall (S&H) across nine modeling variants. An indicator variables analysis determined the necessity of distinct equations for two EZs. Fitting included both linear and nonlinear models. Our comprehensive statistical analysis included goodness-of-fit metrics to evaluate each model variant's performance rigorously. The second modeling variant (SH02) for the SH equation was most effective in the Dry Ecological Zone, showing superior performance in both the fitting and validation phases. Similarly, the third modeling variant (SH03) for the SH equation emerged as the best fit for the Combined Intermediate and Humid Ecological Zones, achieving the lowest overall ranking sum among tested variants. SH02 and SH03 provide reliable and precise volume estimations, allowing for the optimization of forestry management practices for P. occidentalis trees. The SH models outperformed the CV model variants' consistency in parameter estimation. This tailored approach ensures more accurate volume predictions, which is crucial for sustainable management and conservation efforts. [ABSTRACT FROM AUTHOR]

ABSTRACT: A 2-dimensional (2D) egg-shape equation can be used to construct a 3D egg geometry based on the hypothesis that an egg is a solid of revolution, which helps to calculate egg volume and surface area. The parameters in the 2D egg-shape equation are potentially valuable for providing a clue to the ecology and evolution of avian eggs. In this study, the 5-parameter Preston equation (PE), the 4-parameter Troscianko equation (TE), and another 2 egg-shape equations, were compared in describing real 2D egg-shape data of 300 Gallus gallus domesticus eggs and additional 50 eggs that represented the variation in avian egg geometries. Adjusted root-mean-square error was used to quantify each equation's prediction error. Given that the 4 equations are nonlinear, relative curvature measures of nonlinearity were used to assess the extent of nonlinearity in each equation. PE was found to be the best among the 4 equations in terms of adjusted root-mean-square error and minimizing nonlinearity. The empirically determined egg volumes using a graduated cylinder were compared with the predicted egg volumes using the formula for a solid of revolution based on 2D predictions from the 4 egg-shape equations. There were negligible differences in the predicted egg volumes and surface areas among the 4 equations, indicating that these equations are all valid in calculating egg volume and surface area. In addition, we proposed a 5-parameter TE and found that it outperformed the above 4 equations in describing the 2D egg shape of G. gallus, but was less general than PE for other egg shapes. This work provides statistical evidence to show which equation is the best for describing the geometry of avian eggs and nondestructively calculating their volume and surface area, helping to classify poultry eggs into different grades according to the morphological characteristics of the eggs.

By applying a sinusoidal function (as a trigonometric model), this study aimed to introduce this function into ostrich weight development research, using ostrich growth data from the literature and comparing it with some routinely used growth models such as monomolecular, Bridges, Janoschek, logistic, Von Bertalanffy, Richards, Schumacher, Morgan, Chanter, and Weibull. During the fitting of nonlinear regression curves, model performance was evaluated and model behavior was examined. Body weight data of the domestic ostriches used in this study were reported in the Blue Mountain Ostrich Nutrition e-bulletin from three different studies (data sets 1 to 3). In all data sets, body weight was measured monthly from one to twelve months of age. The adjusted coefficient of determination, root mean square error, Akaike's information criterion, and Bayesian information criterion were used to evaluate each model's overall goodness-of-fit to different data profiles. Based on the goodness-of-fit criteria, the sinusoidal model was determined to be the most suitable function for fitting the growth curve of ostriches in data sets 1 and 2. However, both monomolecular and logistic models had the worst fit to the growth curve of ostriches in these data sets. For data set 3, the Weibull model provided the best fit of the growth curve of ostriches, but the sinusoidal function had the worst fit. Absolute growth rate (AGR), calculated using the first derivative of the best model with time showed that AGR values ​​increased with age until days 174, 90, and 68 for data sets 1 to 3, respectively, and then decreased. Overall, this study offers implications for advancing research on ostrich production systems and providing insightful information on the application of alternative nonlinear models in modeling ostrich growth.

This paper introduces the Lomax-exponentiated odds ratio–G (L-EOR–G) distribution, a novel framework designed to adeptly navigate the complexities of modern datasets. It blends theoretical rigor with practical application to surpass the limitations of traditional models in capturing complex data attributes such as heavy tails, shaped curves, and multimodality. Through a comprehensive examination of its theoretical foundations and empirical data analysis, this study lays down a systematic theoretical framework by detailing its statistical properties and validates the distribution's efficacy and robustness in parameter estimation via Monte Carlo simulations. Empirical evidence from real-world datasets further demonstrates the distribution's superior modeling capabilities, supported by compelling various goodness-of-fit tests. The convergence of theoretical precision and practical utility heralds the L-EOR–G distribution as a groundbreaking advancement in statistical modeling, significantly enhancing precision and adaptability. The new model not only addresses a critical need within statistical modeling but also opens avenues for future research, including the development of more sophisticated estimation methods and the adaptation of the model for various data types, thereby promising to refine statistical analysis and interpretation across a wide array of disciplines. [ABSTRACT FROM AUTHOR]

AbstractIn Bayesian analysis, the selection of a prior distribution is typically done by considering each parameter in the model. While this can be convenient, in many scenarios it may be desirable to place a prior on a summary measure of the model instead. In this work, we propose a prior on the model fit, as measured by a Bayesian coefficient of determination (R2), which then induces a prior on the individual parameters. We achieve this by placing a beta prior on R2 and then deriving the induced prior on the global variance parameter for generalized linear mixed models. We derive closed-form expressions in many scenarios and present several approximation strategies when an analytic form is not possible and/or to allow for easier computation. In these situations, we suggest approximating the prior by using a generalized beta prime distribution and provide a simple default prior construction scheme. This approach is quite flexible and can be easily implemented in standard Bayesian software. Lastly, we demonstrate the performance of the method on simulated and real-world data, where the method particularly shines in high-dimensional settings, as well as modeling random effects. [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]

Simple Summary: Feedstuff fiber composition is known to affect digestibility of feeds within the horse. Neutral detergent fiber (NDF) is a chemical measure of plant cell wall material to estimate the amount of feed that will reach the hindgut of the gastrointestinal tract. Acid detergent fiber (ADF) estimates the amount of NDF that is largely unavailable for microbial fermentation in the hindgut of the horse due to the structure of the cell wall. Increases in both NDF and ADF are known to decrease total digestibility in the horse and other species of animals. This study's objective was to determine if feedstuff NDF and ADF could predict simulated digestion in the horse using fecal microbes. Prediction models showed that the interaction of NDF and ADF best predicted total digestion of a feedstuff. However, NDF composition was a poor predictor of fiber digestion by hindgut microbes. Feedstuff ADF strongly predicted fiber degradation in the hindgut as it estimated the amount of cell wall that is resistant to microbial fermentation. The fiber composition of feedstuffs can be used to estimate total digestion and fiber degradation under simulated conditions mimicking the hindgut of the horse. Neutral detergent fiber (NDF) and acid detergent fiber (ADF) composition have been shown to predict in vitro true digestibility (IVTD), in vitro NDF digestibility (IVNDFD), and in vitro ADF digestibility (IVADFD) in ruminants. This study's objective was to estimate in vitro digestibility measures within the DaisyII incubator using equine fecal inoculum from feedstuff NDF and ADF composition. Analyzed feedstuffs included alfalfa hay (Medicago sativa), Coastal Bermudagrass hay, soybean meal, rice bran, hempseed meal, and Bluebonnet® Equilene® Pellets. Data were analyzed using Akaike's information criterion (AIC) within the R Statistical Program©. The highest ranked model for IVTD was the interaction of NDF and ADF: 10003.32 – 0.2904 × NDF − 0.4220 × ADF − 0.0010 × NDF × ADF (Adjusted R2 = 0.959 and AICc = 474.97). Sample IVNDFD was moderately predicted by ADF: 855.15 – 1.5183 × ADF (Adjusted R2 = 0.749 and AICc = 560.82). Feedstuff ADF produced the highest ranked model for IVNDFD: 881.91 – 1.5952 × ADF (Adj. R2 = 0.835 and AICc = 541.33). These results indicate the effectiveness of using feedstuff NDF and ADF composition to predict IVTD, IVNDFD, and IVADFD within equine fecal inoculum. The findings of this study provide better understanding of feedstuff digestibility using equine fecal inoculum, but more research is warranted for validation of the models and the potential impact in vivo. [ABSTRACT FROM AUTHOR]

IntroductionCross frequency coupling (CFC) between electrophysiological signals in the brain is a long-studied phenomenon and its abnormalities have been observed in conditions such as Parkinson's disease and epilepsy. More recently, CFC has been observed in stomach-brain electrophysiologic studies and thus becomes an enticing possible target for diseases involving aberrations of the gut-brain axis. However, current methods of detecting coupling, specifically phase-amplitude coupling (PAC), do not attempt to capture the phase and amplitude statistical relationships.MethodsIn this paper, we first demonstrate a method of modeling these joint statistics with a flexible parametric approach, where we model the conditional distribution of amplitude given phase using a gamma distributed generalized linear model (GLM) with a Fourier basis of regressors. We perform model selection with minimum description length (MDL) principle, demonstrate a method for assessing goodness-of-fit (GOF), and showcase the efficacy of this approach in multiple electroencephalography (EEG) datasets. Secondly, we showcase how we can utilize the mutual information, which operates on the joint distribution, as a canonical measure of coupling, as it is non-zero and non-negative if and only if the phase and amplitude are not statistically independent. In addition, we build off of previous work by Martinez-Cancino et al., and Voytek et al., and show that the information density, evaluated using our method along the given sample path, is a promising measure of time-resolved PAC.ResultsUsing synthetically generated gut-brain coupled signals, we demonstrate that our method outperforms the existing gold-standard methods for detectable low-levels of phase-amplitude coupling through receiver operating characteristic (ROC) curve analysis. To validate our method, we test on invasive EEG recordings by generating comodulograms, and compare our method to the gold standard PAC measure, Modulation Index, demonstrating comparable performance in exploratory analysis. Furthermore, to showcase its use in joint gut-brain electrophysiology data, we generate topoplots of simultaneous high-density EEG and electrgastrography recordings and reproduce seminal work by Richter et al. that demonstrated the existence of gut-brain PAC. Using simulated data, we validate our method for different types of time-varying coupling and then demonstrate its performance to track time-varying PAC in sleep spindle EEG and mismatch negativity (MMN) datasets.ConclusionsOur new measure of PAC using Gamma GLMs and mutual information demonstrates a promising new way to compute PAC values using the full joint distribution on amplitude and phase. Our measure outperforms the most common existing measures of PAC, and show promising results in identifying time varying PAC in electrophysiological datasets. In addition, we provide for using our method with multiple comparisons and show that our measure potentially has more statistical power in electrophysiologic recordings using simultaneous gut-brain datasets.

Wind energy is one of the most sought after worldwide among renewable energy sources. In order to determine the wind potential of a particular site, the wind speed has to be characterized and the Weibull parameters accurately determined. Characterization of wind speed in terms of Weibull parameters for wind energy potential in Nigeria is scarce. Several methods of determining Weibull parameters exist in literature. In this study, five numerical methods, Weibull-two (W), Mixture Weibull (MW), Gamma (G), lognormal (LN) and normal (N), were used to analyse wind speed data from twelve stations measured at 10 m height in order to determine the best method for estimating Weibull parameters for each station and region. The methods were compared and their accuracies were determined by three goodness-of-fit (GOF) tests namely Maximum error of Kolmogorov–Smirnov (K-S), root mean square error (RMSE) and Chi square (χ2). The performances of the methods were ranked on a scale of 1–5 and the results revealed that the MW was ranked the best in all the stations by two of the GOFs tests. It was closely followed by LN. The Weibull and Gamma methods performed poorly. Thus the MW is selected as the best method for determining Weibull parameters accurately and hence wind energy potential for Nigeria.

Exponential-family Random Graph models (ERGM) are widely used in social network analysis when modelling data on the relations between actors. ERGMs are typically interpreted as a snapshot of a network at a given point in time or in a final state. The recently proposed Latent Order Logistic model (LOLOG) directly allows for a latent network formation process. We assess the real-world performance of these models when applied to typical networks modelled by researchers. Specifically, we model data from an ensemble of articles in the journal Social Networks with published ERGM fits, and compare the ERGM fit to a comparable LOLOG fit. We demonstrate that the LOLOG models are, in general, in qualitative agreement with the ERGM models, and provide at least as good a model fit. In addition they are typically faster and easier to fit to data, without the tendency for degeneracy that plagues ERGMs. Our results support the general use of LOLOG models in circumstances where ERGMs are considered.

Pinus occidentalis (Swartz) is the primary timber species in the Dominican Republic (DR). Despite its economic importance, studies conducted on this species are scarce, making it difficult to estimate current inventory levels. This study aims to enhance the accuracy of estimating the total bole volume of P. occidentalis in different ecological zones (EZs) within La Sierra, evaluating and comparing two established volume equations—combined variable (CV) and Schumacher and Hall (S&H) across nine modeling variants. An indicator variables analysis determined the necessity of distinct equations for two EZs. Fitting included both linear and nonlinear models. Our comprehensive statistical analysis included goodness-of-fit metrics to evaluate each model variant’s performance rigorously. The second modeling variant (SH02) for the SH equation was most effective in the Dry Ecological Zone, showing superior performance in both the fitting and validation phases. Similarly, the third modeling variant (SH03) for the SH equation emerged as the best fit for the Combined Intermediate and Humid Ecological Zones, achieving the lowest overall ranking sum among tested variants. SH02 and SH03 provide reliable and precise volume estimations, allowing for the optimization of forestry management practices for P. occidentalis trees. The SH models outperformed the CV model variants’ consistency in parameter estimation. This tailored approach ensures more accurate volume predictions, which is crucial for sustainable management and conservation efforts.

The study aimed to address the modeling challenges associated with non-normal cancer patient characteristics by introducing a novel family of distributions. The analysis focused on datasets encompassing breast cancer, blood cancer, and acute myeloid leukemia patients. Extensive simulation experiments were conducted to compare different estimation techniques and identify the most suitable approach. The results demonstrated that the newly generated family of distributions outperformed the baseline model, providing a closer fit to the cancer patient data and offering valuable insights into patient outcomes and disease treatment.

Data that resides on the surface of a 2-sphere is common in various scientific fields, including physics, earth sciences, astronomy, and psychoacoustics. While some tools and packages exist for performing inferential statistical tests on such data and model fitting, there is currently no comprehensive open-source Python package that implements these tests. sphstat aims to fill this gap by providing an open-source Python package that implements spherical inferential tests and some model-fitting algorithms as catalogued in the authoritative reference by Fisher et al. (1993). Due to the lack of a similar open-source Python package, sphstat has the potential to be widely used in scientific and technical fields where data on the 2-sphere emerges.

Many models are available to fit the curve of a grain size distribution, GSD. The article lists 61 models and 33 comparative studies of models. Examples explain how to extract stratification data from split-spoon samples and how to verify whether a model respects the internal structure of the data. This extraction is essential to determine the field hydraulic properties and in situ behavior of soils. Many tools are available to assess the goodness-of-fit, GOF. This article proves that these tools are not independent. A first new equation is obtained, which links the RMSE (root mean squared error) and (1-R2), R2 being the coefficient of determination. A second new equation is obtained, which links the AIC (Akaike information criterion) and (1-R2) for a GSD. The two novel equations help to derive a new method to assess the GOF for GSDs. The distributions of (1-R2) values clearly classify fitting models as poor, fair, good, or very good. The author’s MDM (modal decomposition method) is the only one to rank very good for any soil. Its basic assumption is verified by individual sublayers, which provide a sound basis. Its explanations are correct for in situ permeability in stratified soils. Most models do not pay attention to the data’s internal structure and distribution of residuals. The MDM respects the internal structure and yields Gaussian residuals for a GSD, which may not be the case of other models. Clear graphs illustrate underfitting and overfitting, and clear rules are given to explain how to use the MDM and extract useful information from a GSD. Free pre-programmed Excel files are made available to readers. [ABSTRACT FROM AUTHOR]

In this paper we suggest a graphical tool for multiple time series modelling with an application in macroeconomies. The asymptotic distribution of the adjusted residual traces introduced in [1, Velilla and Nguyen] is examined and further developed. We propose critical bands of the adjusted residual traces as a useful tool in model selection. An advantage of the method is that visual displays of the critical bands and plots of the adjusted residual traces can assist in selecting a proper multiple time series model. This technique is less dependent on the choice of lag. Several simulations, examples and an application with German time series are included. [ABSTRACT FROM AUTHOR]

Solid-state drives represent the preferred backbone storage solution thanks to their low latency and high throughput capabilities compared to mechanical hard disk drives. The performance of a drive is intertwined with the reliability of the memories; hence, modeling their reliability is an important task to be performed as a support for storage system designers. In the literature, storage developers devise dedicated parametric statistical approaches to model the evolution of the memory's error distribution through well-known statistical frameworks. Some of these well-founded reliability models have a deep connection with the 3D NAND flash technology. In fact, the more precise and accurate the model, the less the probability of incurring storage performance slowdowns. In this work, to avoid some limitations of the parametric methods, a non-parametric approach to test the model goodness-of-fit based on combined permutation tests is carried out. The results show that the electrical characterization of different memory blocks and pages tested provides an FBC feature that can be well-modeled using a multiple regression analysis. [ABSTRACT FROM AUTHOR]

In this work, we derive a geometric goodness-of-fit index similar to R 2 using geometric data analysis techniques. We build the alpha shape complex from the data-cloud projected onto each variable and estimate the area of the complex and its domain. We create an index that measures the difference of area between the alpha shape and the smallest squared window of observation containing the data. By applying ideas similar to those found in the closest neighbor distribution and empty space distribution functions, we can establish when the characterizing geometric features of the point set emerge. This allows for a more precise application for our index. We provide some examples with anomalous patterns to show how our algorithm performs. [ABSTRACT FROM AUTHOR]

This paper considers the construction of a family of discrete distributions with the flexibility to cater for under-, equi- and over-dispersion in count data using a finite mixture model based on standard distributions. We are motivated to introduce this family because its simple finite mixture structure adds flexibility and facilitates application and use in analysis. The family of distributions is exemplified using a mixture of negative binomial and shifted negative binomial distributions. Some basic and probabilistic properties are derived. We perform hypothesis testing for equi-dispersion and simulation studies of their power and consider parameter estimation via maximum likelihood and probability-generating-function-based methods. The utility of the distributions is illustrated via their application to real biological data sets exhibiting under-, equi- and over-dispersion. It is shown that the distribution fits better than the well-known generalized Poisson and COM–Poisson distributions for handling under-, equi- and over-dispersion in count data. [ABSTRACT FROM AUTHOR]

Simulating the probability of type I error is a powerful statistical tool that allows confirming if the statistical test achieves the established nominal level. However, its computational implementation has the drawback of significantly long execution times. Therefore, this article analyzes the performance of two parallel implementations (parRapply and boot) which significantly reduce the execution time of simulations of type I error probability for a goodness-of-fit test for the bivariate Poisson distribution. The results obtained demonstrate how the parallelization strategies accelerate the simulations, reducing the time by 50% to 90% when using 2 to 12 processors running in parallel. This reduction is graphically evidenced as the execution time of the analyzed parallel versions fits almost perfectly (R2≈0.999) to the power model y=apb, where p is the number of processors used, and a>0 and b<0 are the constants of the model. Furthermore, it is shown that the parallelization strategies used scale with an increasing number of processors. All algorithms were implemented in the R programming language, and their code is included at the end of this article.

This paper introduces the Lomax-exponentiated odds ratio–G (L-EOR–G) distribution, a novel framework designed to adeptly navigate the complexities of modern datasets. It blends theoretical rigor with practical application to surpass the limitations of traditional models in capturing complex data attributes such as heavy tails, shaped curves, and multimodality. Through a comprehensive examination of its theoretical foundations and empirical data analysis, this study lays down a systematic theoretical framework by detailing its statistical properties and validates the distribution’s efficacy and robustness in parameter estimation via Monte Carlo simulations. Empirical evidence from real-world datasets further demonstrates the distribution’s superior modeling capabilities, supported by compelling various goodness-of-fit tests. The convergence of theoretical precision and practical utility heralds the L-EOR–G distribution as a groundbreaking advancement in statistical modeling, significantly enhancing precision and adaptability. The new model not only addresses a critical need within statistical modeling but also opens avenues for future research, including the development of more sophisticated estimation methods and the adaptation of the model for various data types, thereby promising to refine statistical analysis and interpretation across a wide array of disciplines.

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.

The Baltic States equity market is a challenge for investors and financial analysts. Unfortunately strong assivity is observed in ``young'' markets, therefore any (Gaussian, α-stable etc) distribution fitting tests (Anderson–Darling, Kolmogorov–Smirnov, etc.) are poorly applicable. Improvement based on mixed distributions is proposed and its adequacy in the Baltic States market is tested. In this paper we use Koutrouvelis goodness-of-fit test and modified χ2 test.

The effectiveness of annual peak discharges under the anthropogenic impact and climate change has significance for disaster management and planning. Therefore, an attempt has been made to study the trend of annual maximum series (AMS) discharges and flood frequency in the Lower Mekong Basin (LMB). The AMS data of five stations in the LMB were procured from the Mekong River Commission for analyses of trends of the AMS and flood frequency. The Mann-Kendall test showed a significant decrease in the magnitude of annual peak floods for all the discharge gauging sites in the LMB. Likewise, the analysis of the annual discharge departure from the mean reveals noteworthy variations and departure (positive and negative) in the annual peak discharges. The goodness-of-fit (GoF) tests showed that Log-Pearson Type-III (LP-III) is the best distribution for AMS of the Mekong River than Gumbel Extreme Value Type-I (GEVI). Therefore, predicted discharges for different return periods and predicted recurrence intervals for average annual discharges (Qm), large floods (Qlf), and maximum annual peak discharge during the recording period (Qmax) by LP-III are trustworthy. The flood frequency curve specified that all the observed discharges were fairly on the best-fitted line and falls between upper and lower confidence limits. Inclusively, the results of the trend in annual peak discharges and flood frequency are consistent and can be used for water management, controlling flood disasters, and flood planning in the LMB.

The study aimed to address the modeling challenges associated with non-normal cancer patient characteristics by introducing a novel family of distributions. The analysis focused on datasets encompassing breast cancer, blood cancer, and acute myeloid leukemia patients. Extensive simulation experiments were conducted to compare different estimation techniques and identify the most suitable approach. The results demonstrated that the newly generated family of distributions outperformed the baseline model, providing a closer fit to the cancer patient data and offering valuable insights into patient outcomes and disease treatment. [ABSTRACT FROM AUTHOR]

The model tree (MT) approach, a data mining technique used to analyse relationships between input and output variables in a disordered and large database, was adopted in this study to predict sediment discharge with field measurement data. The derived models were analysed for accuracy according to the goodness of fit based on training, testing, and modelling processes. When the flow velocity, depth, water surface slope, channel width, and median bed material were selected as the river's system variables, the model results of sediment discharge resembled the measured values. The results demonstrate that developing and using the sediment discharge estimation with the MT constitutes the most effective method if long-term sediment data are of sufficient validity. [ABSTRACT FROM AUTHOR]

Frequency analysis has long been an important theme of hydrology research. Although meteorological techniques (physical approaches) such as radar nowcasting, remote sensing, and forecasting heavy rainfall events using meteorological simulation models are quite effective for urban disaster prevention, statistical and stochastic theories that include frequency analysis, which are usually used in flood control plans, are also valuable for flood control plans for disaster prevention. Master plans for flood control projects in urban areas often use the concept of T-year hydrological values with a T-year return period. A flood control target is a "landside area that is safe against heavy rainfall or floods with a return period of T years". This review emphasizes discussions of parameter estimation of stochastic models and selection of optimal statistical models, which include evaluation of goodness-of-fit techniques of statistical models. Based on those results, the authors criticize Japanese standard procedures recommended by the central government. Consistency between parameter estimation and evaluation of goodness-of-fit is necessary. From this perspective, we recommend using the maximum likelihood method and AIC, both of which are related to Kullback–Leibler divergence. If one prefers using SLSC, we recommend not SLSC itself but SLSC's non-exceedance probability. One important purpose of this review is the introduction of well-used Japanese methods. Because some techniques that are slightly different from the international standard have been used for many years in Japan, we introduce those in the review article. [ABSTRACT FROM AUTHOR]

In terms of heat dissipation, nanofluids with strong thermal conductivity are becoming more and more common, attracting more and more research and attention date. In this study, Al2O3-water nanofluids were studied using molecular dynamics simulations and model parameterization. The dynamic viscosity distribution patterns were obtained at various temperatures (290~360 K), nanoparticle volume fractions (1.24~6.2%), and particle sphericity (0.69~1.0), and an efficient ternary second-order polynomial viscosity prediction model was proposed on the basis of these results. The findings demonstrate the model's goodness-of-fit with a coefficient of determination over 0.96 and a root mean square error under 0.05, as well as its high predictive ability with a maximum relative error between simulated and predicted values under 9%. Using this viscosity prediction model, a subsequent parametric sensitivity study shows that the volume fraction had the most significant impact on viscosity, exhibiting not just a second order effect but also an interacting effect with temperature and sphericity. The relative nanofluid viscosity, which is the ratio of nanofluid viscosity to aqueous base fluid viscosity, exhibits a convex parabolic growth at constant temperature and sphericity and increases more quickly at the same volume fraction the higher the temperature. The viscosity of the nanofluid increases by up to 34% when the volume fraction is equal to 6.28% and the particle sphericity is equal to 1. An efficient viscosity prediction model makes it easier to control important variables to reduce energy consumption during flow and increase its capacity to dissipate heat. [ABSTRACT FROM AUTHOR]

Abstract Biologists routinely fit novel and complex statistical models to push the limits of our understanding. Examples include, but are not limited to, flexible Bayesian approaches (e.g. BUGS, stan), frequentist and likelihood‐based approaches (e.g. packages lme4) and machine learning methods. These software and programs afford the user greater control and flexibility in tailoring complex hierarchical models. However, this level of control and flexibility places a higher degree of responsibility on the user to evaluate the robustness of their statistical inference. To determine how often biologists are running model diagnostics on hierarchical models, we reviewed 50 recently published papers in 2021 in the journal Nature Ecology & Evolution, and we found that the majority of published papers did not report any validation of their hierarchical models, making it difficult for the reader to assess the robustness of their inference. This lack of reporting likely stems from a lack of standardized guidance for best practices and standard methods. Here, we provide a guide to understanding and validating complex models using data simulations. To determine how often biologists use data simulation techniques, we also reviewed 50 recently published papers in 2021 in the journal Methods Ecology & Evolution. We found that 78% of the papers that proposed a new estimation technique, package or model used simulations or generated data in some capacity (18 of 23 papers); but very few of those papers (5 of 23 papers) included either a demonstration that the code could recover realistic estimates for a dataset with known parameters or a demonstration of the statistical properties of the approach. To distil the variety of simulations techniques and their uses, we provide a taxonomy of simulation studies based on the intended inference. We also encourage authors to include a basic validation study whenever novel statistical models are used, which in general, is easy to implement. Simulating data helps a researcher gain a deeper understanding of the models and their assumptions and establish the reliability of their estimation approaches. Wider adoption of data simulations by biologists can improve statistical inference, reliability and open science practices.

Purpose – Time headway (THW) is an essential parameter in traffic safety and is used as a typical control variable by many vehicle control algorithms, especially in safety-critical ADAS and automated driving systems. However, due to the randomness of human drivers, THW cannot be accurately represented, affecting scholars’ more profound research. Design/methodology/approach – In this work, two data sets are used as the experimental data to calculate the goodness-of-fit of 18 commonly used distribution models of THW to select the best distribution model. Subsequently, the characteristic parameters of traffic flow are extracted from the data set, and three variables with higher importance are extracted using the random forest model. Combining the best distribution model parameters of the data set, this study obtained a distribution model with adaptive parameters, and its performance and applicability are verified. Findings – In this work, two data sets are used as the experimental data to calculate the goodness-of-fit of 18 commonly used distribution models of THW to select the best distribution model. Subsequently, the characteristic parameters of traffic flow are extracted from the data set, and three variables with higher importance are extracted using the random forest model. Combining the best distribution model parameters of the data set, this study obtained a distribution model with adaptive parameters, and its performance and applicability are verified. Originality/value – The results show that the proposed model has a 62.7% performance improvement over the distribution model with fixed parameters. Moreover, the parameter function of the distribution model can be regarded as a quantitative analysis of the degree of influence of the traffic flow state on THW.

Pearson's chi-squared test is widely used to test the goodness of fit between categorical data and a given discrete distribution function. When the number of sets of the categorical data, say k, is a fixed integer, Pearson's chi-squared test statistic converges in distribution to a chi-squared distribution with k−1 degrees of freedom when the sample size n goes to infinity. In real applications, the number k often changes with n and may be even much larger than n. By using the martingale techniques, we prove that Pearson's chi-squared test statistic converges to the normal under quite general conditions. We also propose a new test statistic which is more powerful than chi-squared test statistic based on our simulation study. A real application to lottery data is provided to illustrate our methodology. [ABSTRACT FROM AUTHOR]

In this paper, a New Generalized Gamma-Weibull (NGGW) distribution is developed by compounding Weibull and generalized gamma distribution. Some mathematical properties such as moments, R°enyi entropy and order statistics are derived and discussed. The maximum likelihood estimation (MLE) method is used to estimate the model parameters. The proposed model is applied to two real-life datasets to illustrate its performance and flexibility as compared to some other competing distributions. The results obtained show that the new distribution fits each of the data better than the other competing distributions. [ABSTRACT FROM AUTHOR]

We provide a new extension of the exponential distribution with an emphasis on the practical elements of the model. Six different classical estimation methods were applied and compared. The main test was evaluated on complete data using four sets of data. Additionally, four applications and the derivation of the new Nikulin statistic test for the new probability model under the censored situation are described. Both tests were evaluated through simulation experiments on complete data and on artificial and censored data. In addition, a set of simulation experiments were presented, which were used and employed to evaluate the original statistical test and the new modified statistical test based on statistical controls in the evaluation processes. [ABSTRACT FROM AUTHOR]

We propose a class of goodness-of-fit test procedures for arbitrary parametric families of circular distributions with unknown parameters. The tests make use of the specific form of the characteristic function of the family being tested, and are shown to be consistent. We derive the asymptotic null distribution and suggest that the new method be implemented using a bootstrap resampling technique that approximates this distribution consistently. As an illustration, we then specialize this method to testing whether a given data set is from the von Mises distribution, a model that is commonly used and for which considerable theory has been developed. An extensive Monte Carlo study is carried out to compare the new tests with other existing omnibus tests for this model. An application involving five real data sets is provided in order to illustrate the new procedure.

Background: Data with ordinal categories occur in many diverse areas, but methodologies for modeling ordinal data lag severely behind equivalent methodologies for continuous data. There are advantages to using a model specifically developed for ordinal data, such as making fewer assumptions and having greater power for inference. Methods: The ordered stereotype model (OSM) is an ordinal regression model that is more flexible than the popular proportional odds ordinal model. The primary benefit of the OSM is that it uses numeric encoding of the ordinal response categories without assuming the categories are equally-spaced. Results: This article summarizes two recent advances in the OSM: (1) three novel tests to assess goodness-of-fit; (2) a new Generalized Estimating Equations approach to estimate the model for longitudinal studies. These methods use the new spacing of the ordinal categories indicated by the estimated score parameters of the OSM. Conclusions: The recent advances presented can be applied to several fields. We illustrate their use with the well-known arthritis clinical trial dataset. These advances fill a gap in methodologies available for ordinal responses and may be useful for practitioners in many applied fields.

Parametric techniques commonly rely on specific distributional assumptions. It is therefore fundamental to preliminarily identify the eventual violations of such assumptions. Therefore, appropriate testing procedures are required for this purpose to deal with a the goodness-of-fit (GoF) problem. This task can be quite challenging, especially with small sample sizes and multivariate data. Previous studiesshowed how a GoF problem can be easily represented through a traditional two-sample system of hypotheses. Following this idea, in this paper, we propose a multi-aspect permutation-based test to deal with the multivariate goodness-of-fit, taking advantage of the nonparametric combination (NPC) methodology. A simulation study is then conducted to evaluate the performance of our proposal and to identify the eventual critical scenarios. Finally, a real data application is considered.

A new and simple blockwise empirical likelihood moment-based procedure to test if a stationary autoregressive process is Gaussian has been proposed. The proposed test utilizes the skewness and kurtosis moment constraints to develop the test statistic. The test nonparametrically accommodates the dependence in the time series data whilst exhibiting some useful properties of empirical likelihood, such as the Wilks theorem with the test statistic having a chi-square limiting distribution. A Monte Carlo simulation study shows that our proposed test has good control of type I error. The finite sample performance of the proposed test is evaluated and compared to some selected competitor tests for different sample sizes and a variety of alternative applied distributions by means of a Monte Carlo study. The results reveal that our proposed test is on average superior under the log-normal and chi-square alternatives for small to large sample sizes. Some real data studies further revealed the applicability and robustness of our proposed test in practice. [ABSTRACT FROM AUTHOR]

In this paper, we propose a flexible and general family of distributions based on an original power-exponential transformation approach. We call it the modified generalized-G (MGG) family. The elegance and significance of this family lie in the ability to modify the standard distributions by changing their functional forms without adding new parameters, by compounding two distributions, or by adding one or two shape parameters. The aim of this modification is to provide flexible shapes for the corresponding probability functions. In particular, the distributions of the MGG family can possess increasing, constant, decreasing, "unimodal", or "bathtub-shaped" hazard rate functions, which are ideal for fitting several real data sets encountered in applied fields. Some members of the MGG family are proposed for special distributions. Following that, the uniform distribution is chosen as a baseline distribution to yield the modified uniform (MU) distribution with the goal of efficiently modeling measures with bounded values. Some useful key properties of the MU distribution are determined. The estimation of the unknown parameters of the MU model is discussed using seven methods, and then, a simulation study is carried out to explore the performance of the estimates. The flexibility of this model is illustrated by the analysis of two real-life data sets. When compared to fair and well-known competitor models in contemporary literature, better-fitting results are obtained for the new model. [ABSTRACT FROM AUTHOR]