Discrete Order Statistics- A Review

Discrete Order Statistics - A Review provides a comprehensive analysis of the fundamental distribution theory of discrete order statistics. The book addresses important topics such as recursion relationships and identities for order statistics in the i.i.d. case and delves into specific discrete distributions in detail. The introductory chapter outlines the historical development of discrete order statistics. The second chapter focuses on the distributions of order statistics and their dependency structure, including the distributions of order statistics from a randomly drawn sample without replacement. The third chapter presents various recursion relationships and identities for the single and product moments of order statistics in a sample of size n from any discrete distribution. These insights enable efficient calculation of the moments of order statistics, requiring only a few moments from previous samples.