Accession Number : ADA185628

Title :   On Selecting the Best of K Lognormal Distributions.

Descriptive Note : Technical rept.,

Corporate Author : PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS

Personal Author(s) : Gupta, Shanti S ; Miescke, Klaus J

PDF Url : ADA185628

Report Date : Aug 1987

Pagination or Media Count : 20

Abstract : For k lognormal populations, which differ only in one certain parameter theta, the problem of finding the population with largest value of theta is considered. For two-parameter lognormal families, several natural choices of theta are treated, where the problem can be solved, through logarithmic transformation of the observations, within the framework of estimating parameters in k, possibly restricted, normal populations. For three-parameter lognormal families, this standard approach of selecting in terms of natural estimators fails to work if theta is the guaranteed lifetime. For this case, a selection procedure is derived which is based on an L-statistic which has the smallest asymptotic variance. Of importance here is that it is location equivariant, whereas it does not matter what it actually estimates. Comparisons are made with other suitable selection rules, through the asymptotic relative efficiencies, as well as in an example of intermediate sample sizes. In the latter, it is seen that the selection rule, which is based on the sample minima, compares favorably. Keywords: Random variables; Normal distribution.

Descriptors :   *NORMAL DISTRIBUTION, *POPULATION, *SELECTION, LIMITATIONS, LOGARITHM FUNCTIONS, RANDOM VARIABLES

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE