Date of Award

12-2002

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Dr. Michael R. Stoline

Second Advisor

Dr. J.C. Wang

Third Advisor

Dr. Joseph McKean

Fourth Advisor

Dr. Magdelena Niewiadomska-Bugaj

Abstract

The main objective of this dissertation is to estimate the mean /x and standard deviation cr of a normal population from left-censored samples. We have developed new methods for calculating estimates for the mean and standard deviation of a normal population from left-censored samples. Some of these methods based on traditional estimating procedures. A new method of obtaining the Cohen maximum likelihood estimates for fx and cr without the aid of an auxiliary table will be introduced. This new method will be used to extend Cohen table of estimating the Cohen A-parameter that is required for calculating the maximum likelihood estimates via Cohen’s method. Methods for obtaining closed form expressions for calculating estimates of a normal population parameters n and a from singly-left-censored, doubly-left-censored and multiply-left-censored samples is introduced. These methods based on replacing left-censored observations with the same censoring limit by a non-constant value in the complete d a ta likelihood function. An extension of Cohen’s method for calculating the maximum likelihood estimates of a normal population parameters [x and a from doubly-left-censored samples will be introduced and examined. We investigate and compare these methods over many real and simulated data sets. The absolute and mean squared errors are used to compare the ability of estimators obtained via the new methods to recover the true mean and standard deviation of the censored parent distribution.

Comments

Fifth Advisor: Dr. Theodore Chester, Jr.

Access Setting

Dissertation-Open Access

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