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A note on a characterization of the generalized log-logistic distribution

✍ Scribed by Mohammed A. El-Saidi; Karan P. Singh; Alfred A. Bartolucci

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 215 KB
Volume: 1
Category: Article
ISSN: 1180-4009
DOI: 10.1002/env.3170010403

No coin nor oath required. For personal study only.

✦ Synopsis

The log-logistic distribution (LLD) is very useful in a wide variety of applications, especially in the analysis of survival data Cox and Snell 1989). The LLD is very similar in sha.pe to the log-normal distribution, however it has the advantage of having simple algebraic expressions for its survivor and hazard functions and a closed form for its distribution function. It is therefore more convenient than the log-normal distribution in handling censored data. However, due to the symmetry of the log-logistic distribution, it may be inappropriate for modelling censored survival date, especially for the cases where the hazard rate is skewed or heavily tailed. In this article we present a generalization of the LLD and refer to this as the generalized log-logistic distribution (GLLD). The suggested GLLD reflects the skewness and the structure of the heavy tail and generally shows some improvement over the LLD. In addition, we generalize a result characterizing the log-logistic distribution given by Shoukri, and introduce two characterization theorems of the GLLD.

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