Theoretical Properties and Estimation In Weighted Weibull and Related Distributions

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.

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (open access)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2010

Author dc:creator

• Roman, Ryan

Contributors dc:contributor

• Charles Champ
• Hani Samawi

• ETD
• Weighted distribution
• Weibull distribution
• Weighted Weibull distribution
• Mathematics

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/665

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-1665