Exponential Order Statistics and Some Combinatorial Identities

P. Vellaisamy

Published 2016-04-10Version 1

We consider the k-th order statistic from unit exponential distribution and, by computing its Laplace transform, show that it can be represented as sum of independent exponential rvs. Our proof is simple and different. It readily proves that the standardized exponential spacings also follow unit exponential distribution. Another advantage of our approach is that by computing the Laplace transform of the k-th order statistic in two different ways, we derive several interesting combinatorial identities. A probabilistic interpretation of these identities and their generalizations are also given.