Nonparametric Selection of the Smallest-Dispersion Population

SYNOPTIC ABSTRACT

A nonparametric formulation is set up for selecting the best one of k populations. “Best” is defined as the one with the smallest inter(α,β)-range, a measure of dispersion defined by the difference of the β^th quantile and the α^th quantile. The formulation is strictly nonparametric in the sense that the distribution functions are only assumed to be continuous (and are not assumed to be stochastically ordered). The formulation and solution are similar to the solution of the corresponding “central tendency” problem treated by Sobel (1967); tables have not been prepared. Appendix A gives a second-order correction term for the probability of a correct selection. Appendix B deals with selecting a subset containing the best population, and is similar to the solution of the corresponding “central tendency” problem (Rizvi and Sobel (1967), see Appendix C).

Key Words and Phrases:

• Ranking and selection
• interquartile range
• ordering populations by dispersion
• nonparametric ranking
• use of ranks and/or quantiles in statistics