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Candidate:
Abou El-Makarim Abd El-Alim Aboueissa
Degree of:
Doctor of Philosophy
Department: Statistics
Title: New Statistical Methods For The Estimation Of The
Mean And Standard Deviation From Normally Distributed Censored Samples
Committee:
Dr. Michael R. Stoline, Chair
Dr. J. C. Wang
Dr. Joseph McKean
Dr. Magdelana Niewiadomska-Bugaj
Dr. Theodore Chester Jr.
Date: Tuesday, November 5, 2002, 2:00 p.m.-4:00 p.m.,
3302 Rood
Abstract:
The main objective of this dissertation is to estimate the mean m and
standard deviation s 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
m and s without the aid of an auxiliary table will be introduced. This
new method will be used to extend Cohen table of estimating the Cohen
l-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 m and s
from singly-left-censored, doubly-left-censored and multiply-left-censored
samples are introduced. these methods based on replacing left-censored
observations with the same censoring limit by a non-constant value in
the complete data likelihood function. An extension of Cohen's method
for calculating the maximum likelihood estimates of a normal population
parameters m and s 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.
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