Nonparametric procedure for selecting the least nbu population : large sample approach

Abstract

Let π₁, …,π_k be k independent populations with continuous distributions F¹, …, F^k respectively. Hollander and Proschan (1972) proposed as a measure of the NBU-ness of F_iand used it to develop a test of exponentiality versus non-exponential NBU alternatives. In this paper the k populations are compared in terms of ▵_i and we are interested in selecting the population with the largest ▵ value which is defined as the least NBU population. Our procedure is based on the U-statistics J_n(F_i. Which is the unbiased estimator of ▵_i and its large-sample properties. Some applications of the selection procedure to gamma, Weibull and linear failure rate families are discussed.

Keywords:

• ranking and selection
• least NBU
• U-statistic
• two-stage procedure
• Gamma
• Weibull
• mean residual life