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=3n=3, they proved the ordering of the normalized spacings and conjectured that result holds for all nn. We prove this conjecture for n=4n=4 for both spacings and normalized spacings and generalize some results to n>4n>4.