Title of article :
Stochastic Orders for Spacings of Heterogeneous Exponential Random Variables
Author/Authors :
Kochar، نويسنده , , Subhash C and Korwar، نويسنده , , Ramesh، نويسنده ,
Issue Information :
دوفصلنامه با شماره پیاپی سال 1996
Abstract :
We obtain some new results on normalized spacings of independent exponential random variables with possibly different scale parameters. It is shown that the density functions of the individual normalized spacings in this case are mixtures of exponential distributions and, as a result, they are log-convex (and, hence, DFR). G. Pledger and F. Proschan (Optimizing Methods in Statistics(J. S. Rustagi, Ed.), pp. 89–113, Academic Press, New York, 1971), have shown, with the help of a counterexample, that in a sample of size 3 the survival function of the last spacing is not Schur convex. We show that, however, this is true for the second spacing for all sample sizes. G. Pledger and F. Proschan (ibid.) also prove that the spacings are stochastically larger when the scale parameters are unequal than when they are all equal. We strengthen this result from stochastic ordering to likelihood ratio ordering. Some new results on dispersive ordering between the normalized spacings have also been obtained.
Keywords :
Order statistics , log-convex density , Hazard rate ordering , Likelihood ratio ordering , mixture distribution , stochastic ordering , Schur functions , Successive sampling , majorization
Journal title :
Journal of Multivariate Analysis
Journal title :
Journal of Multivariate Analysis