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The convolution of two binomial random variables has appeared in various settings such as a model in machine maintenance and as a Markov chain model. This article presents a bivariate distribution with this convolution of binomials as marginal distributions. This bivariate distribution arises from sampling with partial classification, and this has potentially useful applications in diverse areas. The distribution generalizes the bivariate binomial distribution and its variants. Some properties of the bivariate distribution have been obtained. A mixture formulation of the distribution has been derived which facilitates computation of probabilities and computer sampling. An application to a real data set is presented to illustrate its usefulness in empirical modeling. [ABSTRACT FROM AUTHOR]

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]

New estimators for the scale parameter of the one‐sided Lévy distribution are proposed, which are used for constructing new classes of goodness‐of‐fit (gof) tests, based on the ratio of two estimators of the scale parameter. A Monte Carlo study examines the performance of the new gof tests in controlling type I error rate and evaluates their power performance. The performance of the new classes of gof test is also compared with existing tests. Finally, the applicability of the new gof tests is illustrated using three real data sets. [ABSTRACT FROM AUTHOR]

The normality assumption postulates that empirical data derives from a normal (Gaussian) population. It is a pillar of inferential statistics that enables the theorization of probability functions and the computation of p-values thereof. The breach of this assumption may not impose a formal mathematical constraint on the computation of inferential outputs (e.g., p-values) but may make them inoperable and possibly lead to unethical waste of laboratory animals. Various methods, including statistical tests and qualitative visual examination, can reveal incompatibility with normality and the choice of a procedure should not be trivialized. The following minireview will provide a brief overview of diagrammatical methods and statistical tests commonly employed to evaluate congruence with normality. Special attention will be given to the potential pitfalls associated with their application. Normality is an unachievable ideal that practically never accurately describes natural variables, and detrimental consequences of non-normality may be safeguarded by using large samples. Therefore, the very concept of preliminary normality testing is also, arguably provocatively, questioned. [ABSTRACT FROM AUTHOR]

We introduced DrYFiT (drying data fitting tool), a Microsoft Excel freeware tool to be used for modeling thin‐layer drying of foods, which is available at https://drive.google.com/drive/folders/1ouompmNkmdmw1KMTJUnY0t8dJqSJ9iKv?usp=drive%5flink. There are 12 models in the tool and it can be used without any modeling and programming skills. Time and moisture ratio data can be entered and one of models available (one at a time) can be selected to describe the drying data. Parameter values, standard error of the parameters, p value and a statement that indicates whether the parameter is statistically significant or not (α = 0.05) are reported. Moreover, R2, adjusted R2 and root mean square error values are calculated for each model. Users can instantaneously observe the experimental data and the model fit on the same graph. Residual plot is given next to this graph. It is possible for the users to have the results of all models applied to drying data within a couple of minutes. The results of DrYFiT were compared with some popular software programs used for nonlinear regression and identical values (parameters, standard errors, p values, goodness‐of‐fit statistics) were obtained for 40 datasets. [ABSTRACT FROM AUTHOR]

We develop two significance tests in the setting of functional time series. The null hypothesis of the first test is that the observed data are sampled from a general weak white noise sequence. The null hypothesis of the second test is that the observed data are sampled from a functional autoregressive model of order one (FAR(1)), which can be used as a goodness-of-fit test. Both tests are based on projections on functional principal components. Such projections are used in a great many functional data analysis (FDA) procedures, so our tests are practically relevant. We derive test statistics for each test that are quadratic forms of lagged autocovariance estimates constructed from principal component projections, and establish the requisite asymptotic theory. A simulation study shows that the tests have complimentary advantages against relevant benchmarks. [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]

The assessment of regression models with discrete outcomes is challenging and has many fundamental issues. With discrete outcomes, standard regression model assessment tools such as Pearson and deviance residuals do not follow the conventional reference distribution (normal) under the true model, calling into question the legitimacy of model assessment based on these tools. To fill this gap, we construct a new type of residuals for regression models with general discrete outcomes, including ordinal and count outcomes. The proposed residuals are based on two layers of probability integral transformation. When at least one continuous covariate is available, the proposed residuals closely follow a uniform distribution (or a normal distribution after transformation) under the correctly specified model. One can construct visualizations such as QQ plots to check the overall fit of a model straightforwardly, and the shape of QQ plots can further help identify possible causes of misspecification such as overdispersion. We provide theoretical justification for the proposed residuals by establishing their asymptotic properties. Moreover, in order to assess the mean structure and identify potential covariates, we develop an ordered curve as a supplementary tool, which is based on the comparison between the partial sum of outcomes and of fitted means. Through simulation, we demonstrate empirically that the proposed tools outperform commonly used residuals for various model assessment tasks. We also illustrate the workflow of model assessment using the proposed tools in data analysis. for this article are available online. [ABSTRACT FROM AUTHOR]

Are name statistics in the Gospels and Acts a good test of historicity? Kamil Gregor and Brian Blais, in a recent article of the jshj , argue that the sample of name occurrences in the Gospels and Acts is too small to be determinative and that several statistical anomalies weigh against a positive verdict. Unfortunately, their conclusions result directly from improper testing and questionable data selection. Chi-squared goodness-of-fit testing establishes that name occurrences in the Gospels and Acts fit into their historical context at least as well as those in the works of Josephus. Additionally, they fit better than occurrences derived from ancient fictional sources and occurrences from modern, well-researched historical novels. [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]

Purpose - The paper regards the goodness-of-fit (GOF) tests for doubly truncated continuous data with known truncation points. The first goal of the paper is to derive computing formulas of several test statistics for doubly truncated data, when the number of truncated data is unknown. The second goal is to develop statistical inference procedure based on the derived formulas, which includes information regarding the number of truncated data, when it is available. Research method - The formulas and the inference procedure are developed with the use of the methods proposed by Chernobai, Rachev and Fabozzi [2015], who already developed GOF tests for the left truncated data, when the number of truncated data is unknown. Results - Several tests are developed in case of double truncation. Depending on the chosen truncation points, the tests for left, right or doubly truncated samples might be obtained. When no truncation occurs, the tests are reduced to the complete sample tests. The quality of the tests is assessed on the basis of the FTSE100 return distributions. Originality / value / implications / recommendations - To the best knowledge of the author, computing formulas of the GOF test statistics for doubly truncated distributions with known truncation points, when the number of truncated data is unknown, have not been presented in the literature yet. [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]

We propose new classes of goodness-of-fit tests for the Pareto Type I distribution. These tests are based on a characterization of the Pareto distribution involving order statistics. We derive the limiting null distribution of the tests and also show that the tests are consistent against fixed alternatives. The finite-sample performance of the newly proposed tests are evaluated and compared to some of the existing tests, where it is found that the new tests are competitive in terms of powers. The paper concludes with an application to a real world data set, namely the earnings of the 22 highest paid participants in the inaugural season of LIV golf. [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]

A traditional maritime radar system is utilized for ship detection and tracking through onshore transmitters and receivers. However, it faces challenges when it comes to detecting small boats. In contrast, unmanned surface vehicles (USVs) have been designed to monitor maritime traffic. They excel in detecting vessels of various sizes and enhance the capabilities and resolution of maritime radar systems. Nevertheless, just like conventional radar systems, USVs encounter difficulties due to environmental interference and clutter, affecting the accuracy of target signal detection. This research proposes a comprehensive numerical assessment to tackle the clutter issue associated with USVs. This involves gathering clutter signal data, performing numerical analysis, and employing distribution fitting techniques that leverage mathematical distributions to unravel data complexity. The root mean square error (RMSE) is applied in this analysis to validate the efficacy of the distribution model. The results of this study aim to formulate a clutter model that can enhance radar performance in detecting small vessels within cluttered environments. [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]

We consider goodness-of-fit methods for multivariate symmetric and asymmetric stable Paretian random vectors in arbitrary dimension. The methods are based on the empirical characteristic function and are implemented both in the i.i.d. context as well as for innovations in GARCH models. Asymptotic properties of the proposed procedures are discussed, while the finite-sample properties are illustrated by means of an extensive Monte Carlo study. The procedures are also applied to real data from the financial markets. [ABSTRACT FROM AUTHOR]

We propose a set of goodness-of-fit tests for the semiparametric accelerated failure time (AFT) model, including an omnibus test, a link function test, and a functional form test. This set of tests is derived from a multi-parameter cumulative sum process shown to follow asymptotically a zero-mean Gaussian process. Its evaluation is based on the asymptotically equivalent perturbed version, which enables both graphical and numerical evaluations of the assumed AFT model. Empirical p-values are obtained using the Kolmogorov-type supremum test, which provides a reliable approach for estimating the significance of both proposed un-standardized and standardized test statistics. The proposed procedure is illustrated using the rank-based estimator but is general in the sense that it is directly applicable to some other popular estimators such as induced smoothed rank-based estimator or least-squares estimator that satisfies certain properties. Our proposed methods are rigorously evaluated using extensive simulation experiments that demonstrate their effectiveness in maintaining a Type I error rate and detecting departures from the assumed AFT model in practical sample sizes and censoring rates. Furthermore, the proposed approach is applied to the analysis of the Primary Biliary Cirrhosis data, a widely studied dataset in survival analysis, providing further evidence of the practical usefulness of the proposed methods in real-world scenarios. To make the proposed methods more accessible to researchers, we have implemented them in the R package afttest, which is publicly available on the Comprehensive R Archive Network. [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]

Arthritis is the tenderness and swelling of one or more of the joints. Arthritis therapies are directed mainly at reducing symptoms and improving quality of life. In this article, we introduced a novel four parametric model known as generalized exponentiated unit Gompertz (GEUG) for modeling a clinical trial data which represent the relief or relaxing times of arthritic patients receiving a fixed dosage of certain medication. The key feature of such novel model is the addition of new tuning parameters to unit Gompertz (UG) with the intention of increasing versatility of the UG model. We have derived and studied different statistical and reliable attributes, along with moments and associated measures, uncertainty measures, moments generating functions, complete/incomplete moments, quantile function, survival and hazard functions. A comprehensive simulation analysis is implemented to evaluate the effectiveness of estimation of distribution parameters using numerous well-known classical approaches, like maximum likelihood estimation (MLE), least squares estimation (LSE), weighted least squares estimation (WLSE), Anderson Darling estimation (ADE), right tail Anderson darling estimation (RTADE), and Cramer-Von Mises estimation (CVME). Finally, using a relief time's data on arthritis pain show adaptability of suggested model. The results revealed that it might fit better than other relative models. [ABSTRACT FROM AUTHOR]

A new generalization of the extreme value distribution is presented with its density function, having a wide variety of density and tail shapes for modeling extreme value data. This generalized extreme value distribution will be referred to as the odd generalized extreme value distribution. It is derived by considering the distributions of the odds of the generalized extreme value distribution. Consequently, the new distribution is enlightened by not only having all six families of extreme value distributions; Gumbel, Fréchet, Weibull, reverse‐Gumbel, reverse‐Fréchet, and reverse‐Weibull as submodels but also convenient for modeling bimodal extreme value data that are frequently found in environmental sciences. Basic properties of the distribution, including tail behavior and tail heaviness, are studied. Also, quantile‐based aliases of the new distribution are illustrated using Galton's skewness and Moor's kurtosis plane. The adequacy of the new distribution is illustrated using well‐known goodness‐of‐fit measures. A simulation is performed to validate the estimated risk measures due to repeated data points frequently found in temperature data. The Grand Rapids and well‐known Wooster temperature data sets are analyzed and compared to nine different extreme value distributions to illustrate the new distribution's bimodality, flexibility, and overall fitness. [ABSTRACT FROM AUTHOR]

A copula-based Markov chain model can flexibly capture serial dependence in a time series. However, the computational developments for copula-based Markov models remain insufficient for discrete marginal models compared with continuous ones. In this article, we develop computational methods for a binomial time series under the Clayton and Joe copulas. The methods include the data-generation, parameter estimation, model selection, and goodness-of-fit tests. We implement the methods in our R package Copula.Markov (). We conduct simulations to see the performance of the developed methods. Finally, the proposed method is illustrated by a real dataset. [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]

To evaluate model fit in confirmatory factor analysis, researchers compare goodness-of-fit indices (GOFs) against fixed cutoff values (e.g., CFI >.950) derived from simulation studies. Methodologists have cautioned that cutoffs for GOFs are only valid for settings similar to the simulation scenarios from which cutoffs originated. Despite these warnings, fixed cutoffs for popular GOFs (i.e., χ2, χ2/df, CFI, RMSEA, SRMR) continue to be widely used in applied research. We (1) argue that the practice of using fixed cutoffs needs to be abandoned and (2) review time-honored and emerging alternatives to fixed cutoffs. We first present the most in-depth simulation study to date on the sensitivity of GOFs to model misspecification (i.e., misspecified factor dimensionality and unmodeled cross-loadings) and their susceptibility to further data and analysis characteristics (i.e., estimator, number of indicators, number and distribution of response options, loading magnitude, sample size, and factor correlation). We included all characteristics identified as influential in previous studies. Our simulation enabled us to replicate well-known influences on GOFs and establish hitherto unknown or underappreciated ones. In particular, the magnitude of the factor correlation turned out to moderate the effects of several characteristics on GOFs. Second, to address these problems, we discuss several strategies for assessing model fit that take the dependency of GOFs on the modeling context into account. We highlight tailored (or "dynamic") cutoffs as a way forward. We provide convenient tables with scenario-specific cutoffs as well as regression formulae to predict cutoffs tailored to the empirical setting of interest. [ABSTRACT FROM AUTHOR]

According to the strategy-situation fit hypothesis, it is adaptive to match coping strategies to the controllability of stressors. Although early research generally supported this hypothesis, recent findings have been inconsistent. The goals of this study were to test the strategy-situation fit hypothesis, addressing limitations of past research, and compare it to an alternative hypothesis from the temporal model of control (i.e., to focus on what one can control rather than matching coping strategies to control appraisals). College students (n = 159) completed measures assessing their stressors, coping strategies, stressor controllability, perceived control over present aspects of stressors, and perceived stress. Data were collected via online surveys in Fall 2020. Consistent with the strategy-situation fit hypothesis, using a higher ratio of problem-solving coping for more controllable stressors was associated with less stress. However, using more emotion-focused coping for less controllable stressors was not associated with less stress. In addition, focusing on what one could control in the present was associated with less stress, above and beyond strategy-situation fit. It may be more adaptive to focus on what one can control in the present than to match coping styles to stressor controllability. [ABSTRACT FROM AUTHOR]

Semicontinuous outcomes commonly arise in a wide variety of fields, such as insurance claims, healthcare expenditures, rainfall amounts, and alcohol consumption. Regression models, including Tobit, Tweedie, and two-part models, are widely employed to understand the relationship between semicontinuous outcomes and covariates. Given the potential detrimental consequences of model misspecification, after fitting a regression model, it is of prime importance to check the adequacy of the model. However, due to the point mass at zero, standard diagnostic tools for regression models (eg, deviance and Pearson residuals) are not informative for semicontinuous data. To bridge this gap, we propose a new type of residuals for semicontinuous outcomes that is applicable to general regression models. Under the correctly specified model, the proposed residuals converge to being uniformly distributed, and when the model is misspecified, they significantly depart from this pattern. In addition to in-sample validation, the proposed methodology can also be employed to evaluate predictive distributions. We demonstrate the effectiveness of the proposed tool using health expenditure data from the US Medical Expenditure Panel Survey. [ABSTRACT FROM AUTHOR]

Motivated by the rapidly increasing relevance of virtual material design in the domain of materials science, it has become essential to assess whether topological properties of stochastic models for a spatial tessellation are in accordance with a given dataset. Recently, tools from topological data analysis such as the persistence diagram have allowed to reach profound insights in a variety of application contexts. In this work, we establish the asymptotic normality of a variety of test statistics derived from a tessellation-adapted refinement of the persistence diagram. Since in applications, it is common to work with tessellation data subject to interactions, we establish our main results for Voronoi and Laguerre tessellations whose generators form a Gibbs point process. We elucidate how these conceptual results can be used to derive goodness of fit tests, and then investigate their power in a simulation study. Finally, we apply our testing methodology to a tessellation describing real foam data. [ABSTRACT FROM AUTHOR]

Over-dispersed models are commonly utilized when the variation is more than what the model actually predicts. Since one of the reasons for over-dispersion is the large number of zeros, we employ zero-inflated models instead of more traditional ones to handle this observed occurrence. We present a zero-inflated version of a discrete distribution that was developed in 2021 in our research. Significant statistical characteristics of the suggested model have been identified, such as moments, the over-dispersion feature, generating functions, and related measures, among others. We have carried the parametric estimation using the maximum likelihood estimate. Maximum likelihood estimates are checked for usefulness in a simulation exercise. We evaluated the applicability of our developed model using three real-world data sets. [ABSTRACT FROM AUTHOR]

Randomized response (RR) is a well-known interview technique designed to eliminate evasive response bias that arises from asking sensitive questions. The most frequently asked questions in RR are either whether respondents were "ever" carriers of the sensitive characteristic, or whether they were carriers in a recent period, for instance, "last year". The present paper proposes a design in which both questions are asked, and derives a multinomial model for the joint analysis of these two questions. Compared to the separate analyses with the binomial model, the model makes a useful distinction between last year and former carriers of the sensitive characteristic, it is more efficient in estimating the prevalence of last year carriers, and it has a degree of freedom that allows for a goodness-of-fit test. Furthermore, it is easily extended to a multinomial logistic regression model to investigate the effects of covariates on the prevalence estimates. These benefits are illustrated in two studies on the use of anabolic androgenic steroids in the Netherlands, one using Kuk and one using both the Kuk and forced response. A salient result of our analyses is that the multinomial model provided ample evidence of response biases in the forced response condition. [ABSTRACT FROM AUTHOR]

This paper uses independence-type characterizations to propose a class of test statistics which can be used for testing goodness-of-fit with several classes of null distributions. The resulting tests are consistent against fixed alternatives. Some limiting and small sample properties of the test statistics are explored. In comparison with common universal goodness-of-fit tests, the new tests exhibit better power for most of the alternatives considered, while in comparison with another characterization-based procedure, the new tests provide competitive or comparable power in various simulation settings. The handiness of the proposed tests is demonstrated through several real-data examples. [ABSTRACT FROM AUTHOR]

This paper studies the problem of simultaneously testing that each of k samples, coming from k count variables, were all generated by Poisson laws. The means of those populations may differ. The proposed procedure is designed for large k, which can be bigger than the sample sizes. First, a test is proposed for the case of independent samples, and then the obtained results are extended to dependent data. In each case, the asymptotic distribution of the test statistic is stated under the null hypothesis as well as under alternatives, which allows to study the consistency of the test. Specifically, it is shown that the test statistic is asymptotically free distributed under the null hypothesis. The finite sample performance of the test is studied via simulation. A real data set application is included. [ABSTRACT FROM AUTHOR]

It is crucial to accurately predict the probability distribution of long-term wind speed patterns to evaluate the potential for wind energy. This could involve testing various probability density models to ensure they correctly match the wind speed (WS) characteristics provided. Parametric models have prior distributional assumptions that limit their flexibility and are unsuited for skewed, uni-modal, or multimodal wind regimes. Nonparametric kernel density estimation (KDE) is a data-driven model free from prior distribution assumptions. This study offers a thorough approach to modelling the probability density of hourly WS observations covering 11 locations in Tamil Nadu state in India. The efficacy of nonparametric Gaussian KDE with six bandwidth selectors was examined in modelling WS probability distribution. Additionally, both 1-component and 2-component mixture models are fitted to WS via the maximum likelihood estimation (MLE), the L-moment method (LMOM), and the expectation–maximization approach. The performance of some standard kernel functions, BOX, Epanecknokov, Triweight and Biweight, fitted with the direct-plug-in (DPI) method, are also compared. The model performance of all candidate models is examined thoroughly by employing different goodness-of-fit test measures. Investigation reveals that nonparametric KDE with an unbiased cross-validation approach outperformed all other nonparametric and parametric, uni- and bi-modal distributions for all the stations, except at Kanchipuram. The Gaussian KDE with Silverman rule-of-thumb best fits station Kanchipuram. Also, the best-fitted parametric model, among the 1-component model, outperformed the 2-component mixture models for all selected stations. When comparing the performance of some other kernel densities with DPI bandwidth selectors, it performed better than all parametric models. The hourly WS observation in this case study does not favour any fitted mixture models compared to nonparametric KDE density and 1-component density. Each station's selected model is employed further in estimating non-exceedance probabilities and return periods (RPs). Finally, the design WS quantiles are estimated at different univariate RPs (1, 2, 3, 5, 10, 15, 20, 30, 40, 50, 70, 80, 100 years) for all selected stations. [ABSTRACT FROM AUTHOR]

Performance of classifiers is often measured in terms of average accuracy on test data. Despite being a standard measure, average accuracy fails in characterising the fit of the model to the underlying conditional law of labels given the features vector (⁠ Y ∣ X ⁠), e.g. due to model misspecification, over fitting, and high-dimensionality. In this paper, we consider the fundamental problem of assessing the goodness-of-fit for a general binary classifier. Our framework does not make any parametric assumption on the conditional law Y ∣ X and treats that as a black-box oracle model which can be accessed only through queries. We formulate the goodness-of-fit assessment problem as a tolerance hypothesis testing of the form H 0 : E [ D f (B e r n (η (X)) ‖ B e r n (η ^ (X))) ] ≤ τ where D f represents an f -divergence function, and η (x) ⁠ , η ^ (x) ⁠ , respectively, denote the true and an estimate likelihood for a feature vector x admitting a positive label. We propose a novel test, called G oodness-of-fit with Ra ndomisation and S coring P rocedure (GRASP) for testing H 0 ⁠ , which works in finite sample settings, no matter the features (distribution-free). We also propose model-X GRASP designed for model-X settings where the joint distribution of the features vector is known. Model-X GRASP uses this distributional information to achieve better power. We evaluate the performance of our tests through extensive numerical experiments. [ABSTRACT FROM AUTHOR]

This paper studies the problem of simultaneously testing that each of k independent samples come from a normal population. The means and variances of those populations may differ. The proposed procedures are based on the BHEP test and they allow k to increase, which can be even larger than the sample sizes. [ABSTRACT FROM AUTHOR]

We introduce a new characterization of the Cauchy distribution and propose a class of goodness-of-fit tests for the Cauchy family. The limit distribution is derived in a Hilbert space framework under the null hypothesis. The new tests are consistent against a large class of alternatives. A comparative Monte Carlo simulation study shows that the test is a good competitor for the state of the art procedures, and we apply the tests to log-returns of cryptocurrencies. [ABSTRACT FROM AUTHOR]

We propose a simple approach to assess whether a nonlinear parametric model is appropriate to depict the dose–response relationships and whether two parametric models can be applied to fit a dataset via nonparametric regression. The proposed approach can compensate for the ANOVA, which is sometimes conservative, and is very easy to implement. We illustrate the performance by analyzing experimental examples and a small simulation study. [ABSTRACT FROM AUTHOR]

Within the frequentist structural equation modeling (SEM) framework, adjudicating model quality through measures of fit has been an active area of methodological research. Complicating this conversation is research revealing that a higher quality measurement portion of a SEM can result in poorer estimates of overall model fit than lower quality measurement models, given the same structural misspecifications. Through population analysis and Monte Carlo simulation, we extend the earlier research to recently developed Bayesian SEM measures of fit to evaluate whether these indices are susceptible to the same reliability paradox, in the context of using both uninformative and informative priors. Our results show that the reliability paradox occurs for RMSEA, and to some extent, gamma-hat and PPP (measures of absolute fit); but not CFI or TLI (measures of relative fit), across Bayesian (MCMC) and frequentist (maximum likelihood) SEM frameworks alike. Taken together, these findings indicate that the behavior of these newly adapted Bayesian fit indices map closely to their frequentist analogs. Implications for their utility in identifying incorrectly specified models are discussed. [ABSTRACT FROM AUTHOR]