相关论文: On Stochastic Comparisons of Order Statistics from…

In this paper, we compare extreme order statistics through vector majorization arising from heterogeneous Poisson and geometric random variables. These comparisons are carried out with respect to usual stochastic ordering.

Let $X_1, \ldots , X_n$ be mutually independent exponential random variables with distinct hazard rates $\lambda_1, \ldots , \lambda_n > 0$ and let $Y_1, \ldots, Y_n$ be a random sample from the exponential distribution with hazard rate…

Let $X_1, X_2,\ldots, X_n$ (resp. $Y_1, Y_2,\ldots, Y_n$) be independent random variables such that $X_i$ (resp. $Y_i$) follows generalized exponential distribution with shape parameter $\theta_i$ and scale parameter $\lambda_i$ (resp.…

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…

The second-largest order statistic is of special importance in reliability theory since it represents the time to failure of a $2$-out-of-$n$ system. Consider two $2$-out-of-$n$ systems with heterogeneous random lifetimes. The lifetimes are…

Consider two batches of independent or interdependent exponentiated location-scale distributed heterogeneous random variables. This article investigates ordering results for the second-order statistics from these batches when a vector of…

This manuscript investigates the stochastic comparisons of the second-order statistics from dependent and heterogeneous general semi-parametric family of distributions observations. Some sufficient conditions on the usual stochastic order…

We propose some new results on the comparison of the minimum or maximum order statistic from a random number of non-identical random variables. Under the non-identical set-up, with certain conditions, we prove that random minimum (maximum)…

Let $X_{\lambda _{1}},X_{\lambda _{2}},\ldots ,X_{\lambda _{n}}$ be independent nonnegative random variables with $X_{\lambda _{i}}\sim F(\lambda _{i}t)$, $i=1,\ldots ,n$, where $\lambda _{i}>0$, $i=1,\ldots ,n$ and $F$ is an absolutely…

Dispersive order is a type of variability order for comparing the variability in probability distributions. Star order compares the skewness of probability distributions. This work considers dispersive and star orders of extreme order…

We consider the k-th order statistic from unit exponential distribution and show that it can be represented as a sum of independent exponential random variables. Our proof is simple and different. It readily proves that the standardized…

In this paper, we use a new partial order, called the f-majorization order. The new order includes as special cases the majorization , the reciprocal majorization and the p-larger orders. We provide a comprehensive account of the…

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…

We investigate stochastic comparisons between exponential family distributions and their mixtures with respect to the usual stochastic order, the hazard rate order, the reversed hazard rate order, and the likelihood ratio order. A general…

The following anticoncentration property is proved. The probability that the $k$-order statistic of an arbitrarily correlated jointly Gaussian random vector $X$ with unit variance components lies within an interval of length $\varepsilon$…

In this paper, we focus on stochastic comparisons of extreme order statistics stemming from multiple-outlier scale models with dependence. Archimedean copula is used to model dependence structure among nonnegative random variables.…

In this paper some new characterizing theorems of exponential distribution based on order statistics are presented. Some existing results are generalized and the open conjecture by Arnold and Villasenor is solved.

In this paper, we investigate stochastic comparisons of parallel systems, and obtain two characterization results in this regard. First, we compare a parallel system with independent heterogeneous components to a parallel system with…

In this paper, we study stochastic ordering results between two finite mixtures with single and multiple outliers, assuming subpopulations follow general exponentiated location-scale distributions. For single-outlier mixtures, several…

We consider linear elliptic equations in divergence form with stationary random coefficients of integrable correlations. We characterize the fluctuations of a macroscopic observable of a solution to relative order $\frac{d}{2}$, where $d$…