Multiple Decision Procedures for Tukey's Generalized Lambda Distributions.
PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS
Pagination or Media Count:
Selection and ranking more broadly multiple decision problems arise in many practical situations since it is now well-recognized that the classical tests of homogeneity usually do not provide the answers the experimenter wants. This thesis studies Tukeys lambda distributions as the underlying model for selection and ranking problems. It is known that the family of Tukeys generalized lambda distributions is very broad and contains most well-known distributions as special cases. Chapter 1 deals with selection and ranking problems based on sample medians for the symmetric lambda distributions and gives applications of the lambda family distributions. In Chapter 2, the problems of isotonic selection procedures for the family of lambda distributions and for logistic distributions are considered. Chapter 3 deals with the problem of choosing the optimal score function for different nonparametric procedures proposed by Nagel 1970 and Gupta and McDonald 1970. A Monte Carlo study is carried out. In Chapter 4, a two-stage elimination-type procedure under the Bayesian setting is proposed and its properties are studied. In particular, we use a stopping rule to construct a 1001-2 alpha Highest Posterior Density Credible regions with a common width 2d for the unknown means of selected populations at stage 1. A Monte Carlo study is carried out to examine the performance of the proposed procedure.
- Statistics and Probability