A comparison of the generalized gamma and exponentiated Weibull distributions

Christopher Cox, Matthew Matheson

Research output: Contribution to journalArticle

Abstract

This paper provides a comparison of the three-parameter exponentiated Weibull (EW) and generalized gamma (GG) distributions. The connection between these two different families is that the hazard functions of both have the four standard shapes (increasing, decreasing, bathtub, and arc shaped), and in fact, the shape of the hazard is the same for identical values of the three parameters. For a given EW distribution, we define a matching GG using simulation and also by matching the 5 th, 50 th, and 95 th percentiles. We compare EW and matching GG distributions graphically and using the Kullback-Leibler distance. We find that the survival functions for the EW and matching GG are graphically indistinguishable, and only the hazard functions can sometimes be seen to be slightly different. The Kullback-Leibler distances are very small and decrease with increasing sample size. We conclude that the similarity between the two distributions is striking, and therefore, the EW represents a convenient alternative to the GG with the identical richness of hazard behavior. More importantly, these results suggest that having the four basic hazard shapes may to some extent be an important structural characteristic of any family of distributions.

Original languageEnglish (US)
Pages (from-to)3772-3780
Number of pages9
JournalStatistics in Medicine
Volume33
Issue number21
DOIs
StatePublished - Sep 20 2014

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Weibull Distribution
Weibull
Sample Size
Generalized gamma Distribution
Hazard
Kullback-Leibler Distance
Hazard Function
Survival Function
Percentile
Arc of a curve
Decrease
Alternatives
Simulation
Family
Graphics

Keywords

  • Exponentiated weibull distribution
  • Generalized gamma distribution
  • Parametric survival

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability
  • Medicine(all)

Cite this

A comparison of the generalized gamma and exponentiated Weibull distributions. / Cox, Christopher; Matheson, Matthew.

In: Statistics in Medicine, Vol. 33, No. 21, 20.09.2014, p. 3772-3780.

Research output: Contribution to journalArticle

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