Some new results on stochastic comparisons of spacings from heterogeneous exponential distributions

Abstract

Some new results are obtained on stochastic orderings between random vectors of spacings from heterogeneous exponential distributions and homogeneous ones. Let D1, ..., Dn be the normalized spacings associated with independent exponential random variables X1, ..., Xn, where Xi has hazard rate λi, i=1, 2, ..., n. Let D*1, ..., D*n be the normalized spacings of a random sample Y1, ..., Yn of size n from an exponential distribution with hazard rate λ̄=Σni=1 λi/n. It is shown that for any n ≥ 2, the random vector (D1, ..., Dn) is greater than the random vector (D*1, ..., D*n) in the sense of multivariate likelihood ratio ordering. It also follows from the results proved in this paper that for any j between 2 and n, the survival function of Xj: n - X1 : n is Schur convex. © 1996 Academic Press, Inc.