Doctoral Dissertations

Abstract

"Estimating the reciprocal of a scale parameter by means of frequency moments is investigated. An investigation of the bias and mean squared error is carried out and practical methods for implementing the method of frequency moments in the case of the Cauchy distribution are considered. A two-step estimation procedure is proposed, and a comparison of a one-step and two-step procedure is made. Uniform and normal distributions are considered as prior distributions for the interval width in the frequency moments method and mean squared error is tabulated.

A method to estimate I lxl j f k (x) dx is proposed where f(x) is a probability density function. The method involves the use of the Parzen type density estimators. The estimates are shown to converge almost everywhere.

Pivotal quantities based on estimates of I lx! J f k (x) dx are k developed for estimating location and the reciprocal of scale parameters. Asymptotic distributions are considered for two cases. The results are applied to estimating parameters from the Cauchy distribution"-- Abstract, p. ii

Advisor(s)

Higgins, James J.

Committee Member(s)

Engelhardt, Max
Haddock, Glen
Rigler, A. K.
Bain, Lee J., 1939-

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

University of Missouri--Rolla

Publication Date

1976

Pagination

vi, 121 pages

Note about bibliography

Includes bibliographical references (pages 117-118)

Rights

© 1976 Dolores Marie Halper Tichenor, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Thesis Number

T 4087

Print OCLC #

5985242

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Included in

Mathematics Commons

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