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>

In the literature, orderings of optimal allocations of policy limits and deductibles were established by maximizing the expected utility of wealth of the policyholder. In this paper, by applying the bivariate characterizations of stochastic ordering relations, we reconsider the same model and...

Generalized order statistics have been introduced as a unification of several models of random variables arranged in ascending order of magnitude with different interpretations and statistical applications. The purpose of this note is to investigate conditions on the underlying distribution...

Let W=(W1,...,Wn) be a random vector of n independent random variables, and let R=(R1,...,Rn) be another random vector having the permutation distribution on {1,2,...,n}, independent of W. If the Wi's are ordered in the likelihood ratio order [resp. the hazard rate order, the reversed hazard...

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...

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...