Two New Classes of Generalized Modified Weibull Distributions with Application to Lifetime Data

<p>Weibull distribution and its extended families has been widely studied in lifetime applications. Based on the Weibull-G family of distributions and the exponentiated Weibull distribution, we study in detail two new classes of distributions, namely, Gamma-Weibull-G family of distributions (GWG) and gamma-exponentiated or generalized modified Weibull (GEMW) distribution. Some special models in these new classes are discussed. Statistical properties of these family of distributions, such as expansion of density function, hazard and reverse hazard functions, quantile function, moments, incomplete moments, generating functions, mean deviations, Bonferroni and Lorenz curves and order statistics are presented. For the GEMW, we also present Renyi entropy, estimation of parameters by using method of maximum likelihood, asymptotic confidence intervals and applications using real data.</p>

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (restricted to Georgia Southern)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2014

Author dc:creator

• Pu, Shusen

Contributors dc:contributor

• Charles Champ
• Daniel Linder

• ETD
• Gamma-Weibull-G family of distributions
• gamma-exponentiated modified Weibull distributions
• statistical properties
• uncertainty measure
• Applied Statistics
• Statistical Theory

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/1155

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-2186