Let be a random vector, and denote by X1:n,X2:n,...,Xn:n the corresponding order statistics. When X1,X2,...,Xn represent the lifetimes of n components in a system, the order statistic Xn-k+1:n represents the lifetime of a k-out-of-n system (i.e., a system which works when at least k...

Univariate Birnbaum-Saunders distribution has been used quite effectively to model positively skewed data, especially lifetime data and crack growth data. In this paper, we introduce bivariate Birnbaum-Saunders distribution which is an absolutely continuous distribution whose marginals are...

We consider here the distributions of order statistics and linear combinations of order statistics from an elliptical distribution. We show that these distributions can be expressed as mixtures of unified skew-elliptical distributions, and then use these mixture representations to derive their...

In this paper, we introduce the concepts of average and projected systems associated to a coherent (parent) system. We analyze several aspects of these notions and show that they can be useful tools in studying the performance of coherent systems with non-exchangeable components. We show 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...

A new class of bivariate distributions is presented in this paper. The procedure used in this paper is based on a latent random variable with exponential distribution. The model introduced here is of Marshall-Olkin type. A mixture of the proposed bivariate distributions is also discussed. The...

In this paper, we discuss the problem of testing the homogeneity of several populations when the available data are progressively Type-II censored. Defining for each sample a univariate counting process, we can modify all the methods that were developed during the last two decades (see e.g....

In this paper, a mixture representation for the joint distribution function of progressively Type-II censored order statistics from heterogeneous distributions is established. Applications of this representation to stochastic orderings and inequalities are then illustrated.

Sequential order statistics have been introduced to model sequential k-out-of-n systems which, as an extension of k-out-of-n systems, allow the failure of some components of the system to influence the remaining ones. Based on an independent sample of vectors of sequential order statistics, the...

In this paper, we discuss some basic distributional and asymptotic properties of the Pearson-Kotz Dirichlet multivariate distributions. These distributions, which appear as the limit of conditional Dirichlet random vectors, possess many appealing properties and are interesting from theoretical...