Computing Distributions Of Order Statistics

Recurrence relationships among the distribution functions of order statistics of independent, but not identically distributed, random quantities are derived. These results extend known theory and provide computationally practicable algorithms for a variety of problems. 1. INTRODUCTION Apart from very general theoretical formulae (David, 1981, p.22), little work appears to have been done on the computation of distribution and density functions of order statistics for independent but not identically distributed random variables. In contrast to the independent, identically distributed case, there are considerable computational complications in the independent, non-identically distributed context except in very special cases. Recent work by Boncelet (1987), Balakrishnan (1988), Bapat and Beg (1989), and Balakrishnan, Bendre and Malik (1992), relate the distributions of order statistics in samples of size k to those in samples of sizes k \Gamma 1, generalizing formulae in the standard inde..