Let X1:n=X2:n=...=Xn:n denote the order statistics of random variables X1,X2,...,Xn which are independent but not necessarily identically distributed (INID), and let K1,K2 be two integer-valued random variables, independent of {X1,...,Xn}, such that 1=K1=K2=n. It is shown that if K1 has a...

In some situations, it is difficult and tedious to check notions of dependence properties and dependence orders for multivariate distributions supported on a finite lattice. The purpose of this paper is to utilize a newly developed tool, majorization with respect to weighted trees, to lay out...

Every univariate random variable is smaller, with respect to the ordinary stochastic order and with respect to the hazard rate order, than a right censored version of it. In this paper we attempt to generalize these facts to the multivariate setting. It turns out that in general such comparisons...

For any positive integers m and n, let X1,X2,...,Xm[logical or]n be independent random variables with possibly nonidentical distributions. Let X1:n<=X2:n<=...<=Xn:n be order statistics of random variables X1,X2,...,Xn, and let X1:m<=X2:m<=...<=Xm:m be order statistics of random variables X1,X2,...,Xm. It is shown that (Xj:n,Xj+1:n,...,Xn:n) given Xi:m>y for j-i=max{n-m,0}, and (X1:n,X2:n,...,Xj:n) given Xi:m=y for j-i=min{n-m,0} are all increasing in y with respect to the usual multivariate...</=x2:n<=...<=xn:n>

Let be generalized order statistics based on a continuous distribution function F with parameters k and (m1,...,mn-1). Chen and Hu (2007) [8] investigated the sufficient conditions on F and on the parameters k and mi's such that , where , and is the Shaked-Shanthikumar multivariate dispersive...

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...

Dependence properties of occupancy numbers in the balls and bins experiment are studied. Applying such properties, we investigate further dependence structures of order statistics X1:n[less-than-or-equals, slant]X2:n[less-than-or-equals, slant]...[less-than-or-equals, slant]Xn:n of n independent...

Two multivariate hazard rate stochastic orders are introduced and studied. Their meaning, properties, and relationship to other common stochastic orders are examined and investigated. Some examples that illustrate the theory are detailed. Finally, some applications of the new orders in...

Let X1,X2,...,Xn be independent exponential random variables such that Xi has failure rate [lambda] for i=1,...,p and Xj has failure rate [lambda]* for j=p+1,...,n, where p=1 and q=n-p=1. Denote by Di:n(p,q)=Xi:n-Xi-1:n the ith spacing of the order statistics , where X0:n[reverse not...

A class of multivariate distributions that are mixtures of the positive powers of a max-infinitely divisible distribution are studied. A subclass has the property that all weighted minima or maxima belong to a given location or scale family. By choosing appropriate parametric families for the...