Let X[lambda]1,...,X[lambda]n be independent random variables such that X[lambda]i has exponential distribution with hazard rate [lambda]i, i=1,...,n. It is shown that [summation operator]i=1nX[lambda]i is more dispersed than [summation operator]i=1nX[lambda]i* if ([lambda]1,...,[lambda]n)...

IfX1, ...,Xnare random variables we denote byX(1)[less-than-or-equals, slant]X(2)[less-than-or-equals, slant]...[less-than-or-equals, slant]X(n)their respective order statistics. In the case where the random variables are independent and identically distributed, one may demonstrate very strong...

Generalized order statistics (gOSs) unify the study of order statistics, record values, k-records, Pfeifer's records and several other cases of ordered random variables. In this paper we consider the problem of comparing the degree of dependence between a pair of gOSs thus extending the recent...

Let X1:n[less-than-or-equals, slant]X2:n[less-than-or-equals, slant]...[less-than-or-equals, slant]Xn:n denote the order statistics of a random sample of size n from a probability distribution with distribution function F. Similarly, let Y1:m[less-than-or-equals, slant]Y2:m[less-than-or-equals,...

A composition theorem for functions obeying certain positive ordering is proved. The novelty of the present version is that unlike earlier results which assume both components of the composition to be distributions or survival functions, one of the components is allowed to be negative and...

Let Xi:n denote the ith-order statistic of a random sample of size n from a continuous distribution with distribution function F. It is shown that if F is a decreasing failure rate (DFR) distribution, then Xi:n is less dispersed than Xj:m for i[less-than-or-equals, slant]j and...

Let Xi:n denote the ith order statistic of a random sample of size n from a continuous distribution with cdf F. Sufficient conditions are obtained on F so that Xj:m[less-than-or-equals, slant][small star, filled]Xi:n (hence Xj:m[less-than-or-equals, slant]LorenzXi:n) for i[less-than-or-equals,...