On the conjecture of Kochar and Korwar

In this article, we partially solve a conjecture by Kochar and Korwar (1996) [9] in relation to the normalized spacings of the order statistics of a sample of independent exponential random variables with different scale parameters. In the case of a sample of size n = 3 , they proved the ordering of the normalized spacings and conjectured that result holds for all n . We prove this conjecture for n = 4 for both spacings and normalized spacings and generalize some results to n > 4 .