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This document is a letter to the editor addressing a typographical error in the formulas for the double Pareto-lognormal distribution and the normal-Laplace distribution. The authors clarify that the formulas themselves are correct, but there was an error in the expression of the Mills ratio in the correction by Amini and Rabbani. The authors provide the correct formulas for both distributions and offer further explanation upon request. The authors are affiliated with Juraj Dobrila University of Pula in Croatia. [Extracted from the article]

Note, for instance, that the probabilities given by Castellares et al. ([1]) in page 4 are the same than those shown in expression (9.115) in the book by Johnson et al. ([3]), with the change of parameters Graph HT ht and Graph HT ht Neyman type A (NTA) distribution is frequently used in Biology, Biodosimetry, Environmental Sciences, Epidemiology, etc. A count random variable I X i is said to follow a stopped-sum Poisson, compound Poisson, multiple Poisson or clustered-Poisson distribution, if it can be represented as Graph HT ht where I N i is a Poisson random variable with parameter Graph HT ht and Graph HT ht are independent, identically distributed random variables that are also independent of I N i . [Extracted from the article]

Let F be a continuous distribution function and let Q be its associated quantile function. Let Fh be the kernel estimator of F and Qh that of Q. In this article the L2 right inversion distance between Qh and Q is introduced. It is shown that this distance can be represented in terms of Fh and F, more precisely it is established that the right inversion distance is equal to the conventional integrated squared error between Fh and F. This representation shows that any good bandwidth for Fh is a reasonable bandwidth for Qh and, this fact enables us to suggest methods to choose the smoothing parameter of Q h. Let Q h ̂ c v be the kernel estimator of Q equipped with the global crossvalidation bandwidth h ̂ c v designed for F h. Let Q h ̂ p i be the linear kernel estimator of Q, h ̂ p i being the plug-in bandwidth function. A small scale simulation study presented in this paper contains some examples of distributions for which Q h ̂ c v appears to be superior to Q h ̂ p i . This paper also contains some properties of the classical L2 distance between Qh and Q. [ABSTRACT FROM AUTHOR]

This paper investigates the power performance of five tests, including improved versions of two existing tests, for jointly testing the equality of origin and scale parameters of two samples from a shifted (two-parameter) exponential distribution. The power of the test varies with a shift in either or both of the two parameters. Therefore, a power surface is observed for various tests. Different tests are optimal for different shift sizes. This paper also compares the volume under the five tests' power surfaces to determine an overall best when the shift size is unknown. The generalized likelihood ratio (GLR) test, the Bayoud and Kittaneh test based on Weitzman's overlapping coefficient, recently designed Max and Distance tests, and an improved likelihood-based procedure are compared. The shifted exponential distribution is often an appropriate probability model for the lifetime of a product with a warranty, high voltage current in specific semiconductor transistors, and military personnel vehicles' mileages that failed in operation. The number of survival days for patients with irreversible lung cancer often follows the same distribution. This distribution plays a vital role in the engineering and biomedical sciences. We observe that the newly designed tests and the exact GLR test are almost always preferable to the other tests. We illustrate the proposed exact test procedures with two practical examples. [ABSTRACT FROM AUTHOR]

Presents a response to a letter to the editor of the 'Communications in Statistics--Theory and Methods,' concerning the study 'A multivariate generalization of the power exponential family of distributions.' Reference to other studies on the symmetric Kotz type distribution; Characteristics functions of the power exponential distribution.

Various objective priors have been defined for the common correlation coefficient concerning several bivariate normal populations. In this paper, the proposed approach relies on the asymptotic matching of coverage probabilities corresponding to Bayesian credible intervals considering the corresponding frequentist ones. In the present paper, we focus on several matching criteria including quantile matching, distribution function matching, highest posterior density matching, and matching via inversion of test statistics. In addition, we consider reference priors for different groups of ordering. The proposed methods are investigated and compared between each other in terms of a frequentist coverage probability and then, they are illustrated through a simulation study and two real data examples. [ABSTRACT FROM AUTHOR]

The beta generator technique entails constructing a univariate distribution function as a composite function of two distribution functions. The success of this technique in the univariate setting has prompted research into the possibility of generalization to the bivariate case. Such a generalization, using copulas, has already been proposed in the literature. In this paper, we construct bivariate distribution functions by passing a bivariate distribution function as an argument to the univariate beta distribution function. The class of distributions obtained is identical to an existing class of distributions; however, the elementary elements of the two classes differ (i.e., some distributions are simple to construct using one of the techniques considered and difficult to construct using the other). This paper provides a rigorous derivation of the parameter space of the beta-generated distributions, as well as a result relating to the dependence structure of the marginals. Finally, a practical example is included demonstrating the use of a beta-generated distribution in the modeling of observed losses in the energy market. [ABSTRACT FROM AUTHOR]

In the real world, monitoring the number of transactions between nodes in many networks such as transportation, sales, financial communications, etc. is very important, from which network stakeholders can enjoy significant benefits, as well. The present paper attempts to show a significant reduction in the performance of the statistical methods in detecting network anomalies resulting from losing information due to disregarding the weights of edges in the case of modeling and monitoring weighted networks through using binary models. This paper focuses on and applies normal distribution in a real non social network because the statistical distribution of edges in most weighted networks is normal. The performance of the statistical model in the form of a case study, monitoring electronic components exchange network in a repair company, is described. Using simulation, the ability of the model in detecting network anomalies is compared with the binary model. [ABSTRACT FROM AUTHOR]

In this paper, we present some new ordering properties between two parallel systems comprising general independent heterogeneous components. More precisely, let X 1 , ⋯ , X n and Y 1 , ⋯ , Y n be independent non-negative random variables with X i ∼ F (x ; α i , β i) and Y i ∼ F (x ; θ i , λ i) , i = 1 , ⋯ , n , where F (.) is an absolutely continuous distribution function with reversed hazard rate function r ˜ (·). In this paper, under certain conditions, by using the concept of vector majorization, unordered order, p-majorization and related orders, we discuss stochastic comparisons between parallel systems in the sense of usual stochastic and reversed hazard rate orders. The results developed in this paper generalize some known results in the literature. [ABSTRACT FROM AUTHOR]

The modified Anderson-Darling test statistics have been suggested in testing the highly skewed distributions to detect more possible departures in the right (or left) tail. In this paper, we propose the corresponding modified likelihood ratio test statistics, and compare their performances for the Gumbel distribution with the modified Anderson-Darling test statistics. We also provide the approximate critical values for the generalized extreme value distribution and generalized Pareto distribution where the unknown shape parameter is present. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the tampered random variable (TRV) modeling in multiple step-stress life testing experiments. Here τ 1 < τ 2 < ... < τ k − 1 be (k − 1) prespecified time points and s 1 , s 2 , ... , s k be k prefixed stress levels with si being the stress level in force during the time interval [ τ i − 1 , τ i) for i = 1 , ... , k with τ 0 = 0 and τ k = ∞. We define the tampered random variable T TRV (k) in multiple step-stress scenario and calculate the PDF, CDF, and Hazard rate for the proposed tampered variable T TRV (k) . We derive a general expression for the expectation of T TRV (k) under different number k of stress levels and also obtain some results on stochastic ordering for different k. All these results are obtained under arbitrary baseline (under normal stress condition with stress level s1) life distribution. In particular, we consider exponential distribution with mean θ and Weibull distribution with scale parameter λ and shape parameter α for specific expressions. We also prove some results on equivalence of the TRV modeling with the two other existing models for step-stress life testing, namely, cumulative exposure and tampered failure rate. Finally, we consider some variations of the modeling approach for T TRV (k) to include incorporation of the stress levels, discrete life time, bivariate or multivariate life times. [ABSTRACT FROM AUTHOR]

Interval-censored failure time data often occur in medical follow-up studies among other areas. Regression analysis of linear transformation models with interval-censored data has been investigated by several authors under different contexts, but most of the existing methods assume that the covariates are discrete because these methods rely on the estimation of conditional survival distribution function. Without this assumption, this paper constructs a new generalized estimating equation using the propensity score. The proposed inference procedure does not need to estimate the conditional survival distribution any more and then can be used not only in the discrete but also in the continuous covariate situation. The asymptotic properties of the resulting estimates are given, and an extensive simulation study is performed. Finally, the application to two real datasets is also provided. Key words: Estimating equation; Interval-censored data; Propensity score; Linear transformation model. [ABSTRACT FROM AUTHOR]

In this paper, an economic statistical design for individual samples of quality characteristics which have Exponential distributions presented with variable sampling method. To do this, first the Exponential distribution is transformed to a Normal distribution Using Nelson's approximation, then using Costa and Rahim's economic model, an economic statistical design is obtained for the transformed data. The transition probability matrix and the economic and statistical parameters are formulated. Optimal design parameters (sampling interval, warning and control limits) are determined using Artificial Bee Colony algorithm and a sensitivity study is done for various values of the model parameters. Based on the results, the mentioned method in compared with the fixed ratio sampling method is more effective when a moderate shift occurs. A simulated example is given also to illustrate the proposed design. [ABSTRACT FROM AUTHOR]

The continuous iteration of an exponential-type function allows to describe a whole range of growths between logarithmical and exponential. This principle has been applied to a class of lifetime distributions called Tetration distribution and its subsequent tail has the property to belong to an extremely versatile family, from heavy-tailed to light-tailed. The present paper aims to construct a statistical distribution on the whole real line, based on the same principle. This new distribution, denoted Asymmetric Tetration distribution is obtained by combining a reflection of the Tetration distribution with skewing methods. Two inference methods are developed and compared in terms of performance of their estimators. In addition, an index of tail heaviness at − ∞ is proposed and computed for the most common distributions on the whole real line. Finally, the Asymmetric Tetration distribution is applied to data sets in the finance domain. [ABSTRACT FROM AUTHOR]

Recently, providing a new count regression model is very popular for many researchers. These count regression models are constructed by using a new discrete distribution or one of the existing distributions in the literature. In this paper, we consider a new zero-inflated regression model as an alternative to the zero-inflated regression models. We present two real data applications to illustrate the usefulness of the suggested regression model in modeling data, and compare the competitor models such as Poisson, discrete Lindley, and zero-inflated regression models. We provide a new count regression model which is useful in modeling overdispersed data. [ABSTRACT FROM AUTHOR]

In this paper, we consider a risk model with heavy-tailed claims and Brownian perturbation. Assuming that the distribution function of claim-size is subexponential, and the arrival process of claims is a non stationary process satisfying the principle of large deviation, the asymptotic formula for the ruin probability of this risk model at random time is obtained. [ABSTRACT FROM AUTHOR]

As the duality and complement of the Shannon entropy, the eXtropy is proposed in this years. The eXtropy also can be explained from the perspective of negation, which can be seen as an entropy with one-step negation operation of elements. The Dempster–Shafer theory (DST), as the generalization of probability theory (PT), it can express the more uncertain information than the Bayesian distribution. It contains the uncertainty of the event probability expressed in the Bayesian distribution and the uncertainty of the Bayesian distribution. Based on above, this article proposes a new belief entropy in DST called SU entropy, which is the first belief entropy to use the elements rather than mass functions. And then, a new negation of non-specificity part in DST is proposed, which is the first time to research the negation of non-specificity alone. Finally, a new belief eXtropy was proposed. It is different from the traditional eXtropy thinking, but from the perspective of elements' negation. After verification, it has a satisfying performance in measurement uncertainty in DST. At the end of the paper, we discuss how to understand eXtropy from the perspective of negation, and the future research direction for the new belief eXtropy. [ABSTRACT FROM AUTHOR]

This paper explores the properties of the gap of representative points (RPs) in the sense of minimum mean square error for various univariate statistical distributions. We illustrate the relationship between RPs and doubly truncated mean residual life (DMRL) as well as mean residual life (MRL), which are widely used in survival analysis. The limiting behavior of the gap between the largest two RPs is discussed. In addition, an upper bound of the optimal MSE is given when the univariate random variable X has a domain on finite interval. In simulation studies, the performance of RPs for various distributions is assessed in terms of moment estimation and resampling technique. A brief discussion about the relationship between the tail of the distribution and the gap of RPs is also given. [ABSTRACT FROM AUTHOR]

In this paper, we present new two-stage multiple comparison procedures with the average for location parameters of two-parameter exponential distributions under heteroscedasticity by modifying the existing one proposed by Wu and Wu. Not like one-stage procedures, two-stage multiple comparison procedures are design oriented. A simulation comparison study is done for the new two stage procedures, the old two stage procedures in Wu and Wu and the existing one-stage procedures. The results show that the proposed procedures have shorter confidence length with coverage probabilities closer to the nominal ones than the old two-stage one. At last, an example of four drugs for the treatment for leukemia is studied for illustrative aims. [ABSTRACT FROM AUTHOR]

In this paper, we develop unbiased estimators of the finite population cumulative distribution function (CDF) using two-stage and three-stage cluster sampling. In addition, the ranked-set sampling scheme is also used in the secondary and tertiary sampling frames for further increasing the precision of the CDF estimators. This work is then extended to develop unbiased CDF estimators based on stratified two-stage and three-stage cluster sampling. Moreover, unbiased estimators of the variances of the proposed CDF estimators are also derived. Real datasets are considered to demonstrate the estimation of the CDF under these complex survey sampling schemes. [ABSTRACT FROM AUTHOR]

In this paper, we propose a class of general pretest estimators for the univariate normal mean. The main mathematical idea of the proposed class is the adaptation of randomized tests, where the randomization probability is related to a shrinkage parameter. Consequently, the proposed class includes many existing estimators, such as the pretest, shrinkage, Bayes, and empirical Bayes estimators as special cases. Furthermore, the proposed class can be easily tuned for users by adjusting significance levels and probability function. We derive theoretical properties of the proposed class, such as the expressions for the distribution function, bias, and MSE. Our expressions for the bias and MSE turn out to be simpler than those previously derived for some existing formulas for special cases. We also conduct simulation studies to examine our theoretical results and demonstrate the application of the proposed class through a real dataset. [ABSTRACT FROM AUTHOR]

In this paper, we present a modified one-stage multiple comparison procedure for exponential location parameters with the control under heteroscedasticity including one-sided and two-sided confidence intervals to improve the coverage probability and average confidence length than the old one. These intervals can be used to identify a subset which includes all no-worse-than-the-control treatments in an experimental design and to identify better-than-the-control, worse-than-the- control and not-much-different-from-the-control products in agriculture, stock market, pharmaceutical industries in terms of the minimum guarantee lifetimes. A simulation comparison is done for this modified procedure with the old one in terms of the confidence length and coverage probability. One example is given to demonstrate the proposed modified procedure. [ABSTRACT FROM AUTHOR]

In practical problems connected with forecasting, it sometimes happens that the classical regression estimation is not informative enough to make good predictions of a response variable. This occurs typically when multi-modality, asymmetry, or heteroscedastic noise characterizes the underlying distribution function. In this situation, conditional mode estimation may constitute an alternative method to prediction, because conditional density is more adequate to describe the association between an explanatory data vector and a target variable. In this paper we derive rates of convergence for kernel conditional density and mode functions estimators under psi-weak dependence condition. The asymptotic distribution of the mode function estimator is established and the accuracy of the proposed estimators is illustrated via a simulation study. [ABSTRACT FROM AUTHOR]

The shape of a statistical distribution of data is important in such diverse areas as descriptive analysis, risk analysis, portfolio optimization and strategic decision making. If it is known (or believed) that the probability density function of a random variable is not symmetric, the question of its skewness becomes important. Various methods of assessing skewness have been formulated, but none are totally satisfactory. The classical measurement of skewness is based on higher moments of the random variable about its mean. However, it is well known that those measurements are sensitive to extreme outliers. The implication of the sensitivity is that mean-based metrics of skewness are inefficient, especially in small or medium size sample data. Those mean-based metrics are known as Pearson skewness, Quartile skewness and Octile skewness. All have been devised to try to accommodate for the presence of outliers. However, those test statistics are demonstrably inefficient in the presence of outliers. That inefficiency motivates the approach in this paper; the development of an efficient and more robust skewness metric we call Split Sample Skewness, hereafter referred to as SSS. In this context, efficiency means that the SSS metric requires fewer sample observations than the less efficient metrics cited above to achieve the same level of statistical robustness. The name reflects a methodology that partitions the sample into two subgroups at the median. This paper displays the findings of multiple simulation studies adducing evidence bearing on the efficiency of split ample skewness relative to other measures of skewness. [ABSTRACT FROM AUTHOR]

Copulas have proved to be very successful tools for the flexible modeling of dependence. Bivariate copulas have been deeply researched in recent years, while building higher-dimensional copulas is still recognized to be a difficult task. In this paper, we study the higher-dimensional dependent reliability systems using a type of decomposition called “vine,” by which a multivariate distribution can be decomposed into a cascade of bivariate copulas. Some equations of system reliability for parallel, series, andk-out-of-nsystems are obtained and then decomposed based on C-vine and D-vine copulas. Finally, a shutdown system is considered to illustrate the results obtained in the paper. [ABSTRACT FROM AUTHOR]

Elasticity (or elasticity function) is a new concept that allows us to characterize the probability distribution of any random variable in the same way as characteristic functions and hazard and reverse hazard functions do. Initially defined for continuous variables, it was necessary to extend the definition of elasticity and study its properties in the case of discrete variables. A first attempt to define discrete elasticity is seen in Veres-Ferrer and Pavía (2014a). This paper develops this definition and makes a comparative study of its properties, relating them to the properties shown by discrete hazard and reverse hazard, as both defined in Chechile (2011). Similar to continuous elasticity, one of the most interesting properties of discrete elasticity focuses on the rate of change that this undergoes throughout its support. This paper centers on the study of the rate of change and develops a set of properties that allows us to carry out a detailed analysis. Finally, it addresses the calculation of the elasticity for the resulting variable obtained from discretizing a continuous random variable, distinguishing whether its domain is in real positives or negatives. [ABSTRACT FROM PUBLISHER]

Proportional reversed hazard model and exponentiated distributions have received considerable attention in the statistical literature due to its flexibility. In this paper, we develop the tools for statistical inference of the lifetime distribution of components in a n-component coherent system while the system lifetimes are observed, the system structure is known and the component lifetime follows the proportional reversed hazard model. Different point and interval estimation procedures based on frequentist and Bayesian approaches are developed. The existence and uniqueness of the maximum likelihood estimator are discussed. In addition, two statistical testing procedures, a pivotal quantity approach and a likelihood ratio test, to test whether the exponentiated parameter equals to a particular value are proposed. A numerical example is used to illustrate the methodologies developed in this paper and a Monte Carlo simulation study is employed to evaluate the performance of the statistical inferential procedures. [ABSTRACT FROM AUTHOR]

In this paper, well known disnormality or kurtosis indexes are decomposed into contributions to the measure of disnormality of the center, sides and tails of distributions. The results of this study confirm that the above indexes measure mainly the length and thickness of distribution tails at the expense of the distribution center, which may be more or less peaked or flat. The nature of this decomposition suggests the adoption of new and more appropriate measures of disnormality to capture the various forms in which disnormality occurs. The purpose is to put forward new indexes which are able to measure the aspects of disnormality more appropriately. The proposed indexes are less biased when compared to the structure of well-known indexes and are able to value not only the tail characteristics of distributions, but also those of the sides and the center. [ABSTRACT FROM AUTHOR]

Estimation and prediction of regression models with partition forms are widely applied techniques in statistical inference and data analysis. In this paper, we consider some fundamental inference problems regarding a linear random-effects model (LREM) and its reduced models without statistical distribution assumptions for error terms. We shall present a partition form of LREM and its correctly-reduced models, introduce the consistency concepts of the LREM and its reduced models, define the predictability/estimability of unknown parameters in the LREM and its reduced models, establish the matrix equations and analytical formulas associated with best linear unbiased predictors (BLUPs) and best linear unbiased estimators (BLUEs) of all unknown parameter vectors in the LREM and its reduced models, and present many fundamental decomposition equalities for the BLUPs/BLUEs of all unknown parameters in the LREM and its reduced models. [ABSTRACT FROM AUTHOR]

In this paper, we make use of meta-elliptical copula functions to build a new multivariate distribution with fixed marginal distributions and dependence structure to analyze bounded data. Specifically, we present a flexible p-elliptical multivariate probability distribution in the hypercube (0 , 1) p p with fixed marginal GF-quantile distributions. We then present some illustrative examples and a meta-elliptical multivariate regression model as a flexible alternative to the multivariate normal regression model on unit intervals. A simulation study and real-life data analysis using a Bayesian framework with the extreme-value quantile functions show the flexibility of the proposed meta-multivariate normal regression model for modeling the observed proportion response variables. [ABSTRACT FROM AUTHOR]

In this paper, the problem of Bayesian prediction intervals for a future observations from weighted exponential distribution is concerned. Constant-stress partially accelerated life test under Type-II hybrid censoring scheme of the observed data is used. One- and two-sample Bayesian prediction intervals for a future observations based on Type-II hybrid censored data are derived. Markov Chain Monte Carlo (MCMC) technique is used to find Bayesian predictive intervals because one- and two-sample Bayesian predictive survival function cannot be obtained in closed-form. Finally, some numerical results are presented to illustrate all the inferential results developed in this paper. [ABSTRACT FROM AUTHOR]

This paper considers the problem of structural changes. The empirical likelihood approach is used to estimate change-point in piecewise linear models. And theoretically we establish the consistency of the estimated change-point fraction τ ̂ in piecewise linear models based on residuals. Monte Carlo simulation also shows that the estimated break point fraction τ ̂ converges to its true value τ *. [ABSTRACT FROM AUTHOR]

In this paper, by using a sampling procedure, subjected to length-bias, the distribution function F is estimated by the kernel-type estimator F n s , and also a Berry-Esseen type bound for the smoothed estimator is established in this setting. Further, it is shown that the rate of the normal approximation is O (n − 1 / 6) under some appropriate conditions. [ABSTRACT FROM AUTHOR]

In the context of reliability theory, Eginhard J. Muth introduced in 1977 a continuous probability distribution that has been overlooked in the statistical literature. This paper is devoted to that model. Some statistical measures of the distribution are expressed in closed form and it is shown that the model has increasing failure rate and strictly positive memory. Moreover, the members of this family of distributions can be ordered in terms of the hazard rate order. With respect to the parameter estimation, a problem of identifiability was found via Monte Carlo simulation, which is due to the existence of two shape parameters. Such a problem is overcome if one of the parameters is assumed to be known and then the maximum likelihood method provides accurate estimates. Rainfall data sets from the Australian Bureau of Meteorology are used to illustrate that the model under consideration may be an interesting alternative to other probability distributions commonly used for modeling non-negative real data. [ABSTRACT FROM AUTHOR]

In this paper, we essentially characterize the real power of the convolution set of X + Y, where X and Y ≥ 0 are two independent random variables which have respectively a Bernoulli distribution, with parameter r ∈ (0 , 1) , and an infinitely divisible probability distribution ν. The above problem is equivalent to finding the set of x , y ≥ 0 such that the mapping z ↦ (1 − r + r e z) x (E (e z Y)) y is a Laplace transform of some probability distribution. This class of real power of convolution x is provided and described. The obtained results generalize the case where Y is Gamma or Negative Binomial distributed. [ABSTRACT FROM AUTHOR]

In this paper, when the population is composed of several strata, we deal with the problem of stratified estimation for sensitive attribute by applying the stratified random sampling to the Yennum, Sedory, and Singh (2020) model. In Yennum, Sedory, and Singh (2020) study, they considered the negative binomial and negative hypergeometric distribution as randomization devices. When the size of each stratum was exactly known, the sensitive attribute was estimated by stratification, and the proportional and optimal allocations were examined as a method of allocating samples to each stratum. Also, in case of not knowing the size of each stratum, the sensitive attribute was estimated by using two phase sampling design, and the method of allocating samples to each stratum was also examined. Also, the efficiency between the proposed stratified model of Yennum, Sedory, and Singh (2020) and the existing model of Yennum, Sedory, and Singh (2020) was compared by numerical study for the different choice parameters. [ABSTRACT FROM AUTHOR]

Nonignorable missing data presents a great challenge in statistical applications, since the observed likelihood is not identifiable without any further restrictions. In this paper, we make inference about the differences between the corresponding parameters of two independent samples with nonignorable missing renponse. To address the identifiability issue, we consider a parametric propensity model and utilize group label information as an instrument. Two-step generalized method of moments is applied to estimate the parameters of the propensity based on the instrumental estimating equations, and then population parameters are estimated based on the inverse probability weighting with the estimated propensity. The asymptotic properties of the resulting estimators are established. The finite-sample performance of the differences for the population means, distribution functions and quantiles is studied through simulations, and an application to Korean Labor and Income Panel Study (KLIPS) data set is also presented. [ABSTRACT FROM AUTHOR]

In this paper, we propose a nonparametric Bayesian approach for Lindsey and penalized Gaussian mixtures methods. We compare these methods with the Dirichlet process mixture model. Our approach is a Bayesian nonparametric method not based solely on a parametric family of probability distributions. Thus, the fitted models are more robust to model misspecification. Also, with the Bayesian approach, we have the entire posterior distribution of our parameter of interest; it can be summarized through credible intervals, mean, median, standard deviation, quantiles, etc. The Lindsey, penalized Gaussian mixtures, and Dirichlet process mixture methods are reviewed. The estimations are performed via Markov chain Monte Carlo (MCMC) methods. The penalized Gaussian mixtures method is implemented via Hamiltonian Monte Carlo (HMC). We show that under certain regularity conditions, and as n increases, the posterior distribution of the weights converges to a Normal distribution. Simulation results and data analysis are reported. [ABSTRACT FROM AUTHOR]

In the paper, Karhunen-Loeve expansion and Pythagorean-type distribution identities for the additive two-sided Brownian motion are derived. As the applications of Karhunen-Loeve expansion, the corresponding Laplace transform and small ball probability for the L2 norm are presented. [ABSTRACT FROM AUTHOR]

The variance of the log-likelihood function, which is called varentropy, is a measure of the concentration of information content around the Shannon entropy. This measure is widely applied in finite blocklength information theory and data compression. On the other hand, in the field of statistics, this measure has been used as an alternative of the kurtosis measure for continuous density functions that has a better performance. In this paper, we introduce a method for calculating this measure for the ith order statistic. We study the changes of the varentropy versus i for some distributions and show that in the symmetric distributions, under certain conditions, the median of the order statistics has minimum varentropy. Also, we introduce a new stochastic order based on the varentropy and relationships of it with the other stochastic orders. [ABSTRACT FROM AUTHOR]

In this paper, we consider a location-scale family arising out of Absolutely Continuous Trivariate Exponential (ACTVE) distribution with equal marginal due to Weier and Basu. The distribution of the complete sufficient statistic is obtained by first proving a result on spacings similar to the results of Sukhatme for univariate exponential distribution. The UMRUE with respect to any loss function convex in the second argument of the location – scale parameter is obtained. Following the simultaneous equivariant estimation approach of Edwin Prabhakaran and Chandrasekar, we derive the minimum risk equivariant estimator of the location -scale parameter. Further the equivariant estimation of percentiles of the population is also discussed. UMP tests for ACTVE location-scale family are also derived. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the problem of testing for the equality of k probability distributions defined on (X , B) , where X is a metric space and B is the corresponding Borel σ-field. We introduce a test statistic based on reproducing kernel Hilbert space embeddings and derive its asymptotic distribution under the null hypothesis. Simulations show that the introduced procedure outperforms a known method. [ABSTRACT FROM AUTHOR]

This paper present E-Bayesian and Bayesian estimators of parameters of Poisson inverse exponential distribution (PIED) under Squared error loss function (SELF), General entropy loss function (GELF) and Linear Exponential loss function (LINEX) for progressive type-II censored data with binomial removals (PT-II CBRs). The E-Bayesian and corresponding Bayesian estimators are compared in terms of their risks based on simulated samples from PIED. The proposed methodology is applied to survival time of multiple myeloma patients data. [ABSTRACT FROM AUTHOR]

A moment-based density approximation technique that is based on a generalization of Pearson's system of frequency curves is introduced in this paper. More specifically, the derivative of the logarithm of a continuous density function is expressed as a ratio of polynomials whose coefficients are determined by solving a linear system, and a simple representation of the resulting density function is provided. Additionally, a result relating a sample to its moments is stated and derived. It is then explained that, when used in conjunction with sample moments, the methodology being herein advocated can be utilized for the purpose of modeling data sets, irrespective of their size. Several illustrative examples are presented. [ABSTRACT FROM AUTHOR]

In this article, we study the concomitants of m-generalized order statistics (m-GOS) from iterated Farlie–Gumbel–Morgenstern bivariate distributions, denoted by IFGM (λ , η) , as an extension of several recent papers. Furthermore, the joint distribution of m-GOS of concomitants for this family are studied. Some useful recurrence relations between moments of concomitants are obtained. The generalized exponential distribution is taken a typical case of the possible marginals of the IFGM (λ , η). Finally, the asymptotic behavior of the concomitant's rank for the model ordinary order statistics is studied. [ABSTRACT FROM AUTHOR]

Let X 1 , ... , X n be independent and identically distributed continuous nonnegative random variables and m n = min { X 1 , ... , X n } be the sample minimum. In the present paper, we find the best linear predictors E (m 1 + ... + m n | m j = x) and E (m 1 + ... + m n | m 1 = x 1 , ... , m j = x j) and then analyze their behavior by using simulation in the cases of the standard exponential and uniform distributions. [ABSTRACT FROM AUTHOR]

Bayesian inference is a technique of statistical inference which uses the Bayes' theorem to update the probability distribution as new observed data are available. Uncertain variables are a tool of modeling imprecisely observed quantities associated with experiential information. By integrating Bayesian inference and uncertain variables, this paper proposes an approach of uncertain Bayesian inference to deal with Bayesian inference problems involving imprecise observations. The posterior distribution is derived which gives the probability distribution of an unknown parameter conditional on uncertain observations. And based on the posterior distribution, some inference problems including the point estimation, the interval estimation and the Bayesian prediction, are investigated. [ABSTRACT FROM AUTHOR]

In this paper, the tail properties of the beta-normal distribution and an asymptotic Mills-type ratio are studied. Meanwhile, two applications are presented. The first application obtains the asymptotic behavior of the ratio of probability density functions and the ratio of the tails of the beta-normal and Student's t distributions. The other one considers the asymptotic distribution of the partial maximum of i.i.d. random variables with the beta-normal distribution. [ABSTRACT FROM AUTHOR]

In this paper, we discuss distributional and asymptotic properties of lower exponential spacings obtained from order statistics taken from progressive type-II censoring samples. We find conditions under which the sequence of logarithmic lower exponential spacings converges in probability and with probability one. [ABSTRACT FROM AUTHOR]

This paper treats the problem of stochastic comparisons of two parallel systems with independent heterogeneous components having lifetimes following exponentiated Kumaraswamy-G model. The cases of same and different parent distribution functions are considered. Majorization type partial orders-based sufficient conditions in comparing the largest order statistics in terms of the usual stochastic order, reversed hazard rate order and likelihood ratio order are obtained. The likelihood ratio order among largest order statistics is established for the heterogeneous multiple-outlier exponentiated Kumaraswamy-G models. Several numerical examples are presented for illustrations as well. [ABSTRACT FROM AUTHOR]