Order Statistics from Discrete Distributions

Abstract

Summary. This is a survey of results on order statistics of a random sample taken from a discrete population. We discuss the finite sample distribution theory and characterization results, and study the dependence structure. We also discuss asymptotic results. While some of these results hold for both discrete and continuous populations, emphasis here is on the results which hold specifically for the discrete case. Results on order statistics from the discrete uniform, geometric, binomial, and multinomial distributions are presented and their applications to problems of testing and selection are indicated. The distribution of order statistics of a sample drawn at random without replacement is also covered.

AMS 1980 subject classifications::

• 62G30
• 62E15
• 62E10
• 62E20
• 62D05

Keywords:

• Order statistics
• sample spacings
• discrete distributions
• exact distribution theory
• characterization
• asymptotic distributions
• population quantiles
• discrete uniform
• geometric
• binomial
• multinominal distributions
• sampling without replacement