Selection of the Best from Lognormal Populations Using Type-II Censored Data: Unknown σ_i²Case

Abstract

We consider the problem of selecting the best from k lognormal i 2 i populations using type-II censored samples. The selection parameter is taken to be a linear combination, a + b 2 , since many quantities of interest associated with lognormal can be expressed as exp a + b 2 . Since the known 2 i case has been dealt with elsewhere, the case of unknown 2 i is the focus of this paper. Two-stage procedures are proposed, one for the equal case and the other for the unequal case. The procedure for the equal case, with a simple modification for the subcase when there is no censoring, is comparable to the procedure of Bechhofer et al. (1954), and the comparison is discussed. A discussion on the optimality of the procedures is also included.