ABSTRACT
This chapter presents various results for order statistics based on a random sample of size n from a standard exponential distribution. The exponential distribution plays a prominent role in analyzing many data sets obtained from life-tests, and the use of order statistics in this connection arises quite naturally. The chapter provides a comprehensive summary of various developments that have taken place in this area. It examines some recurrence relations satisfied by single and product moments of order statistics. The chapter deals with relationships of exponential order statistics to order statistics from uniform, geometric, and double exponential distributions. Even though standard exponential order statistics admit such simple explicit expressions for their moments, P. C. Joshi established some recurrence relations satisfied by single and product moments of order statistics. The primary advantage of this recursive method is that it easily extends to the truncated exponential distribution case.
