ℒ¹-Limit of Trimmed Sums of Order Statistics from Location-Scale Distributions with Applications to Type II Censored Data Analysis

Abstract

We derive the 1 -limit of trimmed sums of order statistics from location-scale distributions satisfying certain assumptions. Based on this limit, an approximation to the asymptotic variance of a Best-Asymptotic-Normal (BAN) estimator for the location parameter is developed. Associated formulae are derived for four locationscale distributions commonly used in lifetime data analysis. The approximation is analyzed via the properties of the approximating function and by comparison to the exact values for a special case. Applications are illustrated by applying the approximation to comparing location parameters and to selecting the population with the largest location parameter, using censored samples from location-scale populations.

Selection of the Best from Lognormal Populations Using Type-II Censored Data: Unknown σi2Case

“…The result is based on an application of the Glivenko-Cantelli lemma. For details of the proof, see John and Chen (2006b).…”

“…For doubly type-II censored samples from k (log)normal populations with 2 i known, asymptotic selection procedures have been developed in John and Chen (2006b). The procedures in the latter paper are under some generality, namely, the procedures are for the selection using censored samples from locationscale distributed populations with known scale parameters and satisfying certain conditions.…”