Contributions to selection and ranking theory with special reference to logistic populations

SangHyun Han, Purdue University

Abstract

Selection and ranking (more broadly multiple decision) problems arise in many practical situations where the so-called tests of homogeneity do not provide the answers the experimenter wants. The logistic distribution has been applied in studies of population growth, of mental ability, of bio-assay, of life test data and of biochemical data, but the complete distribution of the sample means and variances of a logistic population has not been obtained yet. In this thesis we study the selection and ranking problems for logistic populations and an elimination type two-stage procedure for selecting the best population using a restricted subset selection rule in its first stage. Chapter 2 deals with the selection and ranking procedures for logistic populations. An excellent approximation to the distribution of the sample means from a logistic population is derived by using the Edgeworth series expansions. Using this approximation, we propose and study a single-stage procedure using the indifference zone approach, two subset selection rules based on sample means and medians respectively for selecting the population with the largest mean from k logistic populations when the common variance is known. Chapter 3 considers an elimination type two-stage procedure for selecting the population with the largest mean from k logistic populations when the common variance is known. A table of the constants needed to implement this procedure is provided and the efficiency of this procedure relative to the single-stage procedure is investigated. Chapter 4 deals with a single-stage restricted subset selection procedure for selecting the population with the largest mean from k logistic populations when the common variance is known. Some properties of this procedure such as monotonicity and consistency are investigated. A new design criterion to get the needed sample size and the constant defining this procedure simultaneously is proposed. Chapter 5 deals with a more flexible two-stage procedure for selecting the best population, which uses a restricted subset selection rule in its first stage and the Bechhofer's natural decision procedure in the second stage, in terms of a set of consistent estimators of the real population parameters, whose distributions form a stochastically increasing family for a given sample size. (Abstract shortened with permission of author.)

Degree

Ph.D.

Advisors

Gupta, Purdue University.

Subject Area

Statistics

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