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Extensions, Generalizations, Characterizations And Testing For Independence Through Infinite Divisibility, Edward Joul Danial

Doctoral Dissertations

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 …