Term of Award

Summer 2010

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Department

Department of Mathematical Sciences

Committee Chair

Broderick O. Oluyede

Committee Member 1

Charles Champ

Committee Member 2

Hani Samawi

Abstract

The Weibull distribution is a well known and common distribution. In this thesis, theoretical properties of weighted Weibull distributions are presented. Properties of the non-weighted Weibull distribution are also reiterated for comparison. The probability density functions, cumulative distribution functions, survival functions, hazard functions and reverse hazard functions are given for each distribution. In addition, Glaser's Lemma is applied to determine the behavior of the hazard functions. The standardized moments, differential entropy, Fisher information and results based on the likelihood function are given for each distribution as well. These results are also shown for the Rayleigh distribution, a special case of the Weibull distribution, and its weighted versions.

Included in

Mathematics Commons

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