JSM 2005 - Toronto

Abstract #304552

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Activity Number: 457
Type: Contributed
Date/Time: Wednesday, August 10, 2005 : 2:00 PM to 3:50 PM
Sponsor: Section on Physical and Engineering Sciences
Abstract - #304552
Title: Generalized Log-logistic Families of Lifetime Distributions
Author(s): James Gleaton*+ and James Lynch
Companies: University of North Florida and University of South Carolina
Address: 4567 St Johns Bluff Road South, Jacksonville, FL, 32224,
Keywords: log-odds rate ; hazard rate ; generalized log-logistic ; linear parallel systems
Abstract:

Given a lifetime distribution H(x), another lifetime distribution may be generated through a generalized log-logistic transformation with a nonnegative parameter K. This type of relationship between lifetime distributions will hold in the following situations: There is a parallel system of components, subjected to an input, which affects all components equally; the component response is proportional to the component input throughout the range of operation of the component to failure; there are subsets of components that differ in the constant of proportionality of response. It is shown that the g.l.l. transformation partitions the set of all lifetime distributions. In each equivalence class, any one member may be considered the generating member. Within each class, there is a strict linear ordering of distributions according to dispersion, with dispersion being a strictly decreasing function of K. It also is shown that, while different members may have different hazard rate classifications, the functional form of the log-odds rate is the same for all of them. Conditions for the existence of moments and moment-generating functions are established.

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