Some New Results on Stochastic Comparisons of Spacings from Heterogeneous Exponential Distributions

Some new results are obtained on stochastic orderings between random vectors of spacings from heterogeneous exponential distributions and homogeneous ones. LetD1, ..., Dnbe the normalized spacings associated with independent exponential random variablesX1, ...,Xn, whereXihas hazard rate[lambda]i,i=1, 2, ..., n. LetD*1, ..., D*nbe the normalized spacings of a random sampleY1, ..., Ynof sizenfrom an exponential distribution with hazard rate[lambda]=[summation operator]ni=1 [lambda]i/n. It is shown that for anyn[greater-or-equal, slanted]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 anyjbetween 2 andn, the survival function ofXj:n-X1:nis Schur convex.