Doctoral Dissertations

Abstract

This dissertation investigates various related topics around the exciting concept: "Infinite Divisibility." First, two intricate distributions, namely, the univariate generalized Waring and the hyper-Poisson are proved to be infinitely and noninfinitely divisible, respectively. Analysis and computer approaches are employed. This itself extends the use of some results introduced by Katti, Steutel and Warde. Secondly, generalizations to Warde, Katti and Steutel's sufficient conditions and related results are achieved. Then, numerical application is presented. Thirdly, characterizations through infinite and finite divisibility are obtained. The Poisson, negative binomial, geometric, Bernoulli and uniform c haracterizations in terms of infinite divisibility are deduced. Some of these are used to deduce corresponding characterizations through finite divisibility; such as those of the Poisson, negative binomial and geometric. These two kinds of characterizations have unique value in testing for independence via infinite and finite divisibility. Some of this is manifested later in the testing part of our dissertation. Finally, a good test through infinite divisibility is constructed; where two classes of infinitely divisible distributions, namely, the logarithmic and Poisson, are tested against two classes of Non infinitely divisible, specifically, the hyper-Poisson and binomial. Hence, infinite divisibility could serve as a new accent in statistics, through which some interesting testing could be accomplished. An area of application is to overcome larvae infestation in farms and similar infestation problems--Abstract, p. ii

Advisor(s)

Shriniwas K. Katti

Committee Member(s)

Max Engelhardt
John C. Kieffer
Lee J. Bain
Howard D. Pyron

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

University of Missouri--Rolla

Publication Date

Summer 1982

Pagination

xiii, 249 pages

Note about bibliography

Includes bibliographical references (pages 123-124)

Rights

© 1982 Edward Joul Danial, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Subject Headings

ProbabilitiesMathematical statisticsLimit theorems (Probability theory)

Thesis Number

T 4826

Print OCLC #

9729895

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Included in

Mathematics Commons

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