This paper studies the multivariate mixed proportional reversed hazard rate model having dependent mixing variables. Stochastic comparison as well as aging properties in this model are investigated, and stochastic monotone properties of the population vector with respect to the mixing vector are...

As one of the criteria for comparing variabilities among distributions, the sample range has attracted considerable attention in past decades. In this paper, we establish stochastic comparison results of sample ranges arising from two sets of heterogeneous exponential samples. It is shown that...

Let X1,...,Xn be independent exponential random variables with respective hazard rates [lambda]1,...,[lambda]n, and let Y1,...,Yn be independent exponential random variables with common hazard rate [lambda]. This paper proves that X2:n, the second order statistic of X1,...,Xn, is larger than...

It is difficult to compute the signature of a coherent system with a large number of components. This paper derives two basic formulas for computing the signature of a system which can be decomposed into two subsystems (modules). As an immediate application, we obtain the formula for computing...

Ordering properties on order statistics from heterogeneous observations have been paid lots of attention. This article devotes to investigating the ordering properties on order statistics from statistically dependent observations. We build the likelihood ratio order and the (reversed) hazard...

A class of generalized bivariate Marshall-Olkin distributions, which includes as special cases the Marshall-Olkin bivariate exponential distribution and the Marshall-Olkin type distribution due to Muliere and Scarsini (1987) [19] are examined in this paper. Stochastic comparison results are...

In this paper, we compare the largest order statistics arising from independent heterogeneous gamma random variables based on the likelihood ratio order. Let X1,…,Xn be independent gamma random variables with Xi having shape parameter r∈(0,1] and scale parameter λi, i=1,…,n, and let Xn:n...

We compare the hazard rate functions of the largest order statistic arising from independent heterogeneous gamma random variables and that arising from i.i.d. gamma random variables. Specifically, let X1,…,Xn be independent gamma random variables with Xi having shape parameter 0r≤1 and scale...

In this paper, we study convolutions of heterogeneous exponential random variables with respect to the mean residual life order. By introducing a new partial order (reciprocal majorization order), we prove that this order between two parameter vectors implies the mean residual life order between...

In this paper, we treat convolutions of heterogeneous geometric random variables with respect to the p-larger order and the hazard rate order. It is shown that the p-larger order between two parameter vectors implies the hazard rate order between convolutions of two heterogeneous geometric...