Term of Award
Spring 2010
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Department of Mathematical Sciences
Committee Chair
Broderick O. Oluyede
Committee Member 1
Charles Champ
Committee Member 2
Hani Samawi
Abstract
The weighted inverse Weibull distribution and the beta-inverse Weibull distribution are considered. Theoretical properties of the inverse Weibull model, weighted inverse Weibull distribution including the hazard function, reverse hazard function, moments, moment generating function, coefficient of variation, coefficient of skewness, coefficient of kurtosis, Fisher information and Shanon entropy are studied. The estimation for the parameters of the length-biased inverse Weibull distribution via maximum likelihood estimation and method of moment estimation techniques are presented, as well as a test for the detection of length-biasedness in the inverse Weibull model. Furthermore, the beta-inverse Weibull distribution which is a weighted distribution is presented, including the cumulative distribution function (cdf), probability density function (pdf), density plots, moments, and the moment generating function. Also, some useful transformations that lead to the generation of observations from the beta-inverse Weibull distribution are derived.
Recommended Citation
Kersey, Jing Xiong, "Weighted Inverse Weibull and Beta-Inverse Weibull Distribution" (2010). Electronic Theses and Dissertations. 661.
https://digitalcommons.georgiasouthern.edu/etd/661
Research Data and Supplementary Material
No
