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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]

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]

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]

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]

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]

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]

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]

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 novel goodness-of-fit tests for the Weibull distribution with unknown parameters. These tests are based on an alternative characterizing representation of the Laplace transform related to the density approach in the context of Stein's method. Asymptotic theory of the tests is derived, including the limit null distribution, the behaviour under contiguous alternatives, the validity of the parametric bootstrap procedure, and consistency of the tests against a large class of alternatives. A Monte Carlo simulation study shows the competitiveness of the new procedure. Finally, the procedure is applied to real data examples taken from the materials science. [ABSTRACT FROM AUTHOR]

Assessment of extreme rainfall events (ERE) is crucial for disaster management. Numerical weather prediction (NWP) model-based predictions often fail to predict the extremes. This could be due to several reasons, including insufficient model resolution to capture the sub-grid scale processes, inadequate high-quality observational data for assimilation, uncertainty in initial conditions and approximations in model physics. Estimation of rainfall for different return periods (RP) using extreme value analysis (EVA) can aid in better decision-making. RP of an event indicates its probability and rarity over the region. The current study shows how EVA can be used to supplement model predictions. This study uses the high-resolution (0.25×0.25) gridded observed rainfall data from India Meteorological Department (IMD), which has been available for 117 years (1901–2017). The generalised extreme value (GEV) distribution is applied with suitable goodness-of-fit tests. Rainfall amounts corresponding to 100-year RP are estimated using EVA over the entire data period (1901–2017) and three epochs (1901–1940, 1941–1980, and 1981–2017). The results indicate increasing rainfall amounts corresponding to 100-year RP. Similarly, rainfall amounts for 25, 50, 100, and 200-year RP over Kerala are computed to compare with the extremely heavy rainfall (≤21 cm/day) amounts reported during JJAS 2018 and 2019. Further, this approach supplements the operational forecasts of NCUM-G model forecasts. [ABSTRACT FROM AUTHOR]

We propose a new class of goodness‐of‐fit tests for the logistic distribution based on a characterization related to the density approach in the context of Stein's method. This characterization‐based test is a first of its kind for the logistic distribution. The asymptotic null distribution of the test statistic is derived and it is shown that the test is consistent against fixed alternatives. The finite sample power performance of the newly proposed class of tests is compared to various existing tests by means of a Monte Carlo study. It is found that this new class of tests are especially powerful when the alternative distributions are heavy tailed, like Student's t and Cauchy, or for skew alternatives such as the log‐normal, gamma and chi‐square distributions. [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]

We revisit the family of goodness-of-fit tests for exponentiality based on the mean residual life time proposed by Baringhaus and Henze [(2008), 'A New Weighted Integral Goodness-of-Fit Statistic for Exponentiality', Statistics & Probability Letters, 78(8), 1006–1016]. We motivate the test statistic by a characterisation of Shanbhag [(1970), 'The Characterizations for Exponential and Geometric Distributions', Journal of the American Statistical Association, 65(331), 1256–1259] and provide an alternative representation, which leads to simple and short proofs for the known theory and an easy to access covariance structure of the limiting Gaussian process under the null hypothesis. Explicit formulas for the eigenvalues and eigenfunctions of the operator associated with the limit covariance are given using results on weighted Brownian bridges. In addition, we derive further asymptotic theory under fixed alternatives as well as approximate Bahadur efficiencies, which provide an insight into the choice of the tuning parameter with regard to the power performance of the tests. [ABSTRACT FROM AUTHOR]

Probability predictions from binary regressions or machine learning methods ought to be calibrated: if an event is predicted to occur with probability |$x$|⁠ , it should materialize with approximately that frequency, which means that the so-called calibration curve |$p(\cdot)$| should equal the identity, i.e. |$p(x) = x$| for all |$x$| in the unit interval. We propose honest calibration assessment based on novel confidence bands for the calibration curve, which are valid subject to only the natural assumption of isotonicity. Besides testing the classical goodness-of-fit null hypothesis of perfect calibration, our bands facilitate inverted goodness-of-fit tests whose rejection allows for the sought-after conclusion of a sufficiently well-specified model. We show that our bands have a finite-sample coverage guarantee, are narrower than those of existing approaches, and adapt to the local smoothness of the calibration curve |$p$| and the local variance of the binary observations. In an application to modelling predictions of an infant having low birth weight, the bounds give informative insights into model calibration. [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]

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]

Numerous disciplines, including engineering, public health, sociology, psychology, and epidemiology, are particularly interested in the analysis and modelling of zero truncated count data. As a result, we suggest a novel and straightforward structural model in this study called zero truncated new discrete distribution. We examine its statistical properties including probability mass function, cumulative function, and moments. The parametric estimation of the zero-truncated new discrete distribution is explained by Maximum Likelihood Estimation method and, to investigate its performance, a simulation study is proposed. The importance of the distribution is evaluated using two real-world data sets as well as one simulated data set and the model comparison is made on the basis of AIC and BIC criterions. [ABSTRACT FROM AUTHOR]

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]

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]

Imperfect repair (IR) modelling has attracted a lot of attention during the last decades. To assess and predict repairable systems' reliability, analysts have to choose among a plethora of models: renewal processes, non‐homogeneous Poisson processes (NHPPs), Brown–Proschan, Kijima, ARA, ARI, Quasi‐Renewal (QR), Trend‐Renewal and so forth. Choosing an appropriate model for a given failures, dataset is an important practical issue. The fit of an IR model can be assessed using goodness‐of‐fit (GoF) tests but very few have been proposed and a good fit to past data does not guarantee good reliability predictions. This work proposes general GoF tests for IR models based on sequential (or on‐line) assessment of times‐to‐failures forecasts. The suggested predictive‐sequential (or prequential) GoF tests have a low computational complexity and a common test statistic for several IR models. These tests have been proved to be asymptotically distribution‐free (ADF) for renewal and power‐law processes (PLPs). Our numerical simulations and preliminary theoretical results highly suggest that this ADF property still holds for several other IR models. The prequential tests are much easier to use than the already known bootstrap tests, and a simulation study shows that they are also slightly more powerful. The simulations also show that the prequential tests are powerful to identify classes of similar appropriate models but are much less powerful to distinguish models belonging to the same class. A comparison of MTTF estimates show that models from the same class give close reliability predictions and that the tests are able to reject models which would yield to dramatic errors in reliability predictions. [ABSTRACT FROM AUTHOR]

This paper studies the goodness of fit test for the bivariate Hermite distribution. Specifically, we propose and study a Cramér–von Mises-type test based on the empirical probability generation function. The bootstrap can be used to consistently estimate the null distribution of the test statistics. A simulation study investigates the goodness of the bootstrap approach for finite sample sizes. [ABSTRACT FROM AUTHOR]

In this article, we present a review of important results and statistical applications obtained or generalized by Canadian pioneers and their collaborators, for empirical processes of independent and identically distributed observations, pseudo‐observations, and time series. In particular, we consider weak convergence and strong approximations results, as well as tests for model adequacy such as tests of independence, tests of goodness‐of‐fit, tests of change point, and tests of serial dependence for time series. We also consider applications of empirical processes of interacting particle systems for the approximation of measure‐valued processes. [ABSTRACT FROM AUTHOR]

We propose a spatiotemporal point process model that enhances the classical Epidemic‐Type Aftershock Sequence (ETAS) model. This is achieved with the introduction of a renewal main‐shock arrival process and we call this extension the renewal ETAS (RETAS) model. This modification is similar in spirit to the renewal Hawkes (RHawkes) process but the conditional intensity process supports a spatial component. It empowers the main‐shock intensity to reset upon the arrival of main‐shocks. This allows for heavier clustering of main‐shocks than the classical spatiotemporal ETAS model. We introduce a likelihood evaluation algorithm for parameter estimation and provide a novel procedure to evaluate the fitted model's goodness‐of‐fit (GOF) based on a sequential application of the Rosenblatt transformation. A simulation algorithm for the RETAS model is outlined and used to validate the numerical performance of the likelihood evaluation algorithm and GOF test procedure. We illustrate the proposed model and methods on various earthquake catalogues around the world each with distinctly different seismic activity. These catalogues demonstrate the RETAS model's additional flexibility in comparison to the classical spatiotemporal ETAS model and emphasizes the potential for superior modelling and forecasting of seismicity. [ABSTRACT FROM AUTHOR]

We propose and study new goodness-of-fit tests for the Rayleigh distribution based on a characterization involving a conditional expectation. The asymptotic properties of the tests are explored and the performance of the new tests are evaluated and compared to that of existing tests by means of a Monte Carlo study. It is found that the newly proposed tests perform satisfactory compared to the competitor tests. [ABSTRACT FROM AUTHOR]

We consider goodness–of–fit tests for the distribution of the composed error in Stochastic Frontier Models. The proposed test statistic utilizes the characteristic function of the composed error term, and is formulated as a weighted integral of properly standardized data. The new test statistic is shown to be consistent and computationally convenient. Simulation results are presented whereby resampling versions of the new tests are compared to classical goodness–of–fit methods. [ABSTRACT FROM AUTHOR]

In this paper, the applicability of the sine modified Lindley distribution, recently introduced in the statistical literature, is highlighted via the goodness-of-fit approach on biological data. In particular, it is shown to be beneficial in estimating and modeling the life periods of growth hormone guinea pigs given tubercle bacilli, growth hormone treatment for children, and the size of tumors in cancer patients. We anticipate that our model will be effective in modeling the survival times of diseases related to cancer. The R codes for the figures, as well as information on how the data are processed, are provided. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Classical continuous goodness-of-fit (GOF) testing is employed for examining whether the data come from an assumed parametric model. In many cases, GOF tests assume a uniform null distribution and examine extreme values of the order statistics of the samples. Many of these statistics can be expressed by a function of the order statistics and the p-values amount to a joint probability statement based on the uniform order statistics. In this paper, we utilize Steck's recursion method and propose two high precision computing algorithms to compute the p-values for these GOF statistics. The numerical difficulties in implementing Steck's method are discussed and compared with solutions provided in high precision libraries. [ABSTRACT FROM AUTHOR]

We propose a new goodness-of-fit test for the Rayleigh distribution which is based on a distributional fixed-point property of the Stein characterization. The limiting null distribution of the test is derived and the consistency against fixed alternatives is also shown. The results of a finite-sample comparison is presented, where we compare the power performance of the new test to a variety of other tests. In addition to existing tests for the Rayleigh distribution we also exploit the link between the exponential and Rayleigh distributions. This allows us to include some powerful tests developed specifically for the exponential distribution in the comparison. It is found that the new test outperforms competing tests for many of the alternative distributions. Interestingly, the highest estimated power, against all alternative distributions considered, is obtained by one of the tests specifically developed for the Rayleigh distribution and not by any of the exponentiality tests based on the transformed data. The use of the new test is illustrated on a real-world COVID-19 data set. [ABSTRACT FROM AUTHOR]

Classical tests of goodness of fit aim to validate the conformity of a postulated model to the data under study. Given their inferential nature, they can be considered a crucial step in confirmatory data analysis. In their standard formulation, however, they do not allow exploring how the hypothesized model deviates from the truth nor do they provide any insight into how the rejected model could be improved to better fit the data. The main goal of this work is to establish a comprehensive framework for goodness of fit which naturally integrates modeling, estimation, inference and graphics. Modeling and estimation focus on a novel formulation of smooth tests that easily extends to arbitrary distributions, either continuous or discrete. Inference and adequate post-selection adjustments are performed via a specially designed smoothed bootstrap and the results are summarized via an exhaustive graphical tool called CD-plot. Technical proofs, codes and data are provided in the . [ABSTRACT FROM AUTHOR]

In a masonry veneer wall system, tie strengths and stiffnesses vary randomly and so are not consistent for all ties throughout the wall. To ensure an economical and safe design, this paper uses tie calibration experimental approach in accordance with the standard AS2699.1 to investigate the tie failure load under compression and tension loading. Probabilistic wall tie characterisations are accomplished by estimating the mean, coefficient of variation and characteristic axial compressive and tensile strength from 50 specimens. The displacement across the cavity is recorded, which resulted the complete load versus displacement response. Using the maximum likelihood method, a range of probability distributions are fitted to tie strengths at different displacement histogram data sets, and a best-fitted probability distribution is selected for each case. The inverse cumulative distribution function plots are also used along with the Anderson-Darling test to infer a goodness-of-fit for the probabilistic models. An extensive statistical correlation analysis is also conducted to check the correlation between different tie strengths and associated displacement for both compression and tension loading. Based on the findings, a wall tie constitutive law is proposed to define probabilistic tie behaviour in numerical modelling. [ABSTRACT FROM AUTHOR]

When releasing data to the public, a vital concern is the risk of exposing personal information of the individuals who have contributed to the data set. Many mechanisms have been proposed to protect individual privacy, though less attention has been dedicated to practically conducting valid inferences on the altered privacy-protected data sets. For frequency tables, the privacyprotection-oriented perturbations often lead to negative cell counts. Releasing such tables can undermine users' confidence in the usefulness of such data sets. This paper focuses on releasing one-way frequency tables. We recommend an optimal mechanism that satisfies β-differential privacy (DP) without suffering from having negative cell counts. The procedure is optimal in the sense that the expected utility is maximized under a given privacy constraint. Valid inference procedures for testing goodness-of-fit are also developed for the DP privacy-protected data. In particular, we propose a de-biased test statistic for the optimal procedure and derive its asymptotic distribution. In addition, we also introduce testing procedures for the commonly used Laplace and Gaussian mechanisms, which provide a good finite sample approximation for the null distributions. Moreover, the decaying rate requirements for the privacy regime are provided for the inference procedures to be valid. We further consider common users' practices such as merging related or neighboring cells or integrating statistical information obtained across different data sources and derive valid testing procedures when these operations occur. Simulation studies show that our inference results hold well even when the sample size is relatively small. Comparisons with the current field standards, including the Laplace, the Gaussian (both with/without post-processing of replacing negative cell counts with zeros), and the Binomial-Beta McClure-Reiter mechanisms, are carried out. In the end, we apply our method to the National Center for Early Development and Learning's (NCEDL) multi-state studies data to demonstrate its practical applicability. [ABSTRACT FROM AUTHOR]

There have been numerous tests proposed to determine whether or not the exponential model is suitable for a given data set. In this article, we propose a new test statistic based on spacings to test whether the general progressive Type-II censored samples are from exponential distribution. The null distribution of the test statistic is discussed and it could be approximated by the standard normal distribution. Meanwhile, we propose an approximate method for calculating the expectation and variance of samples under null hypothesis and corresponding power function is also given. Then, a simulation study is conducted. We calculate the approximation of the power based on normality and compare the results with those obtained by Monte Carlo simulation under different alternatives with distinct types of hazard function. Results of simulation study disclose that the power properties of this statistic by using Monte Carlo simulation are better for the alternatives with monotone increasing hazard function, and otherwise, normal approximation simulation results are relatively better. Finally, two illustrative examples are presented. [ABSTRACT FROM AUTHOR]

Within the field of geostatistics, Gaussian processes are a staple for modelling spatial and spatio-temporal data. Statistical literature is rich with estimation methods for the mean and covariance of such processes (in both frequentist and Bayesian contexts). Considerably less attention has been paid to developing goodness-of-fit tests for assessment of model adequacy. Jun et al. (Environmetrics 25(8):584–595, 2014) introduced a statistical test that uses pivotal discrepancy measures to assess goodness-of-fit in the Bayesian context. We present a modification and generalization of their statistical test. The initial method involves spatial partitioning of the data, followed by evaluation of a pivotal discrepancy measure at each posterior draw to obtain a posterior distribution of pivotal statistics. Order statistics from this distribution are used to obtain approximate p-values. Jun et al. (Environmetrics 25(8):584–595, 2014) use arbitrary partitions based on pre-existing spatial boundaries. The partitions are made to be of equal size. Our contribution is two-fold. We use K-means clustering to create the spatial partitions and we generalise Jun et al.'s approach to incorporate unequal partition sizes. Observations from a spatial or spatio-temporal process are partitioned using an appropriate feature vector that incorporates the geographic location of the observations into subsets (not necessarily of the same size). The method's viability is illustrated in a simulation study, and in an application to hoki (Macruronus novaezelandiae) catch data from a survey of the sub-Antarctic region. [ABSTRACT FROM AUTHOR]

Parametric models for analysis of survival data with possible crossing of hazard rates related with two treatment groups are introduced. Strategy for survival improvement through application of time-varying treatment is discussed. Complete and right-censored data with possible confounding covariates are considered. Estimators of the crossing points are given. Chi-square type goodness-of-fit tests for the considered models are given. Parametric tests for the absence of crossing of survival functions (and also for crossing of the hazard functions) hypothesis are proposed. [ABSTRACT FROM AUTHOR]

In this article, we propose several statistics to conduct goodness-of-fit tests for Rayleigh distribution based on progressively Type-II censored data, where a cumulative entropy and its upper and lower bounds as well as the sample spacings are used respectively, and the corresponding statistics are denoted by TE, TU, TL and TS. Especially, the null distribution of TS test statistic is derived. Then the developed methods are extended to the case of one-parameter Weibull model. The respective performance of these statistics is explored against different alternatives, and the power comparisons with some existing goodness-of-fit test statistics are studied via a wide range of Monte Carlo simulations. The results reveal that TS is more effective than the others in most cases; all test statistics have a remarkable performance for the alternative hypothesis with decreasing hazard function. Finally, the proposed statistics are applied in an illustrative example. [ABSTRACT FROM AUTHOR]

The bivariate Poisson distribution is commonly used to model bivariate count data. In this paper we study a goodness-of-fit test for this distribution. We also provide a review of the existing tests for the bivariate Poisson distribution, and its multivariate extension. The proposed test is consistent against any fixed alternative. It is also able to detect local alternatives converging to the null at the rate n − 1 2 . The bootstrap can be employed to consistently estimate the null distribution of the test statistic. Through a simulation study we investigated the goodness of the bootstrap approximation and the power for finite sample sizes. [ABSTRACT FROM AUTHOR]

A new empirical likelihood ratio test for normality based on moment relations is outlined. The proposed test is developed following the works of Shan et al. (2010). Our proposed test is simple and efficient and it is easy to implement in various statistical packages with the computation of the test statistic not requiring ordering of observations. Monte Carlo simulations revealed that the proposed test proved to be superior under asymmetric alternatives considered as well as symmetric alternatives defined on (0,1). Real data examples are given as well as recommendations of future research areas. [ABSTRACT FROM AUTHOR]

The functional linear model with functional response (FLMFR) is one of the most fundamental models to assess the relation between two functional random variables. In this article, we propose a novel goodness‐of‐fit test for the FLMFR against a general, unspecified, alternative. The test statistic is formulated in terms of a Cramér–von Mises norm over a doubly projected empirical process which, using geometrical arguments, yields an easy‐to‐compute weighted quadratic norm. A resampling procedure calibrates the test through a wild bootstrap on the residuals and the use of convenient computational procedures. As a sideways contribution, and since the statistic requires a reliable estimator of the FLMFR, we discuss and compare several regularized estimators, providing a new one specifically convenient for our test. The finite sample behavior of the test is illustrated via a simulation study. Also, the new proposal is compared with previous significance tests. Two novel real data sets illustrate the application of the new test. [ABSTRACT FROM AUTHOR]

We consider a variety of tests for testing goodness–of–fit in a parametric Cox proportional hazards (PH) and accelerated failure time (AFT) model in the presence of Type–II right censoring. The testing procedures considered can be divided in two categories: an approach involving transforming the data to a complete sample and an approach using test statistics that can directly accommodate Type-II right censoring. The power of the proposed tests are compared through a Monte Carlo study for various scenarios. It is found that both approaches are useful for testing exponentiality if the censoring proportion in a data set is lower than 30%, but that it is recommended to use the approach that first transforms the sample to a complete sample when one encounters higher censoring proportions. [ABSTRACT FROM AUTHOR]

Background: Academic emotions (e.g., enjoyment of learning or anxiety) play a significant role in academic performance and educational choices. An important factor explaining academic emotions can be students' temperament and the goodness-of-fit between their temperament and their social environment, including parents. Objective: This study investigated the unique and interactive effects of early adolescents' and their parents' temperament types on adolescents' academic emotions in literacy and mathematics. Method: The participants in the study consisted of 690 adolescent–parent dyads. Parents rated their own and their adolescents' temperaments, and adolescents reported their positive and negative emotions in literacy and mathematics. Results: The results showed that adolescents' temperament type was significantly related to their negative emotions in both school subjects. Adolescents with an undercontrolled temperament reported more anger compared to adolescents with a resilient or overcontrolled temperament, and more anxiety, shame, and hopelessness compared to resilient adolescents. In addition, undercontrolled adolescents reported more boredom in mathematics than resilient or overcontrolled adolescents. The parents' temperament type was related to positive emotions. Adolescents of resilient parents reported greater pride in mathematics than adolescents of undercontrolled or overcontrolled parents and higher hope in mathematics than adolescents of overcontrolled parents. Finally, overcontrolled adolescents with a resilient or overcontrolled parent reported higher enjoyment of mathematics and literacy in comparison to overcontrolled adolescents with an undercontrolled parent. Conclusions: The findings of the study provide new knowledge about the role of temperament in the school context by showing that differences in temperamental reactivity and regulation relate to adolescents' academic emotions. [ABSTRACT FROM AUTHOR]

In this study, a wind speed analysis is conducted using Reanalysis wind speed data for the height of 50 meters using five probability distributions that were tested and compared using the Maximum Likelihood Method (MLM) for estimating the distributions parameters and three goodness-of-fit tests for selecting the best fitting one, namely the Akaike Information Criterion (AIC), The Bayesian Information Criterion (BIC) and the Anderson-Darling (AD). The wind roses, histograms, wind map and the wind power density maps were established. For complementarity between solar and wind, an assessment based on energy fluctuations is adopted and a new complementarity metric is proposed. Using reanalysis data and satellite-based data, a wind turbine model and a PV systems output data are used. This method uses a combination of normalization and a distance metric. Firstly, the outliers are removed, then the daily power output data for PV and Wind turbine are scaled using the minimum-maximum normalization. This normalization transforms both energies data into the same range of 0-1, where the minimum is equal to 0 and the maximum is equal to 1, while conserving its structure, hence, this allows for comparison between the two sources and identify days with high complementarity, for instance when one source is close to 1 and the other is close to zero. For complementarity assessment, the Euclidean distance is adopted. This distance is calculated for each between the normalized values of both sources, and it is between 0 and 1; higher distance indicates high complementarity level. [ABSTRACT FROM AUTHOR]

Multilevel modelling is a novel approach to analyse data which consist of a hierarchical or a nested structure. With advancements in multilevel modelling, there has been an advancement in the estimation techniques and also in goodness-of-fit tests which are vital to assess the fit of a model. However, these goodness-of-fit tests are not as yet tested to be suitable for models estimated using different estimation techniques. This study aims to conduct a comparison of methods of estimations for use in a goodness-of-fit test which is developed for binary response multilevel models. The comparison is based upon the mathematical background, extensive simulations and an application to a real-life dataset. [ABSTRACT FROM AUTHOR]