Some New Results on Stochastic Comparisons of Spacings from Heterogeneous Exponential Distributions
✍ Scribed by Subhash Kochar; Javier Rojo
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 383 KB
- Volume
- 59
- Category
- Article
- ISSN
- 0047-259X
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✦ Synopsis
Some new results are obtained on stochastic orderings between random vectors of spacings from heterogeneous exponential distributions and homogeneous ones. Let D 1 , ..., D n be the normalized spacings associated with independent exponential random variables X 1 , ..., X n , where X i has hazard rate * i , i=1, 2, ..., n. Let D* 1 , ..., D* n be the normalized spacings of a random sample Y 1 , ..., Y n of size n from an exponential distribution with hazard rate * = n i=1 * i Ân. It is shown that for any n 2, the random vector (D 1 , ..., D n ) 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 X j: n &X 1: n is Schur convex.