Related papers: Ordering properties of the smallest order statisti…
In the literature of stochastic orders, one rarely finds results that can be considered as criteria for the non-comparability of random variables. In this paper, we provide results that enable researchers to use simple tools to conclude…
Modeling is a challenging topic and using parametric models is an important stage to reach flexible function for modeling. Weibull distribution has two parameters which are shape $\alpha$ and scale $\beta$. In this study, bimodality…
Fitting mixture distributions is needed in applications where data belongs to inhomogeneous populations comprising homogeneous sub-populations. The mixing proportions of the sub populations are in general unknown and need to be estimated as…
This paper extends the empirical minimum divergence approach for models which satisfy linear constraints with respect to the probability measure of the underlying variable (moment constraints) to the case where such constraints pertain to…
Let $B(n,p)$ denote a binomial random variable with parameters $n$ and $p$. Chv\'{a}tal's theorem says that for any fixed $n\geq 2$, as $m$ ranges over $\{0,\ldots,n\}$, the probability $q_m:=P(B(n,m/n)\leq m)$ is the smallest when $m$ is…
Comparing two groups under different conditions is ubiquitous in the biomedical sciences. In many cases, samples from the two groups can be naturally paired; for example a pair of samples may come from the same individual under the two…
A new notion of stochastic ordering is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of…
We consider testing marginal independence versus conditional independence in a trivariate Gaussian setting. The two models are non-nested and their intersection is a union of two marginal independences. We consider two sequences of such…
The first step in statistical reliability studies of coherent systems is the estimation of the reliability of each system component. For the cases of parallel and series systems the literature is abundant. It seems that the present paper is…
In this manuscript, we study stochastic comparisons of the second-order statistics from dependent or independent observations with modified proportional hazard rates models. First, we establish the usual stochastic order of the second-order…
A theoretical framework is presented for a (copula-based) notion of dissimilarity between continuous random vectors and its main properties are studied. The proposed dissimilarity assigns the smallest value to a pair of random vectors that…
In reliability and life data analysis, the Weibull distribution is widely used to accommodate more data characteristics by changing the values of the parameters. We frequently observe many zeros or close to zero data points in reliability…
Given two independent samples of non-negative random variables with unknown distribution functions $F$ and $G$, respectively, we introduce and discuss two tests for the hypothesis that $F$ is less than or equal to $G$ in increasing convex…
Let $X_1, \ldots, X_n$ be independent non-negative random variables with cumulative distribution functions $F_1,F_2,\ldots,F_n$, each satisfying certain (rather mild) conditions. We show that the median of $k$-th smallest order statistic of…
In this paper, we have obtained conditions on parameters that result in dispersive ordering and star ordering among two unequal sets of random variables from Proportional hazard rate and Proportional reversed hazard rate family of…
As a motivating problem, we aim to study some special aspects of the marginal distributions of the order statistics for exchangeable and (more generally) for minimally stable non-negative random variables $T_{1},...,T_{r}$. In any case, we…
We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. Given samples from $s$ distributions, $p_1, p_2, \ldots, p_s$, we design testers for the…
The aim of the present work is to investigate the performances of a specific Bayesian control chart used to compare two processes. The chart monitors the ratio of the percentiles of a key characteristic associated with the processes. The…
In this article, we focus on stochastic orders to compare the magnitudes of two parallel systems from Weibull distributions when one set of scale parameters majorizes the other. The new results obtained here extend some of those proved by…
Recently, Chowdhury and Kundu [6] compared two parallel systems of heterogeneous independent log-Lindley distributed components using the concept of vector majorization and related orders. Under the same set-up, this paper derives some…