Hazard Rate Functions for Distributions Generated from a Two-Parameter Weibull Distribution by a Generalized Log-Logistic Transformation

• Activity Number: 538
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): James Gleaton*+
• Companies: Univ of North Florida
• Keywords: hazard rate ; Weibull distribution ; reliability ; Generalized log-Logistic

Abstract

The GLLW2 family of lifetime distributions is obtained from a 2-parameter Weibull distribution through a generalized log-logistic (GLL) transformation, for non-negative values of the transformation parameter. The log-odds rate for a lifetime distribution is the sum of the hazard rate function and the reverse hazard rate function. It is easily shown that all GLLW2 distributions generated from a particular 2-parameter Weibull distribution have the same log-odds rate, apart from a multiplicative constant, which is the transformation parameter. However, the hazard rate may differ in functional form and class across distributions in the family. We here examine the behavior of the hazard rate function as it depends on the three parameters - the two parameters of the Weibull distribution and the GLL transformation parameter.