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A new generalization of Weibull distribution with application to a breast cancer data set
Author(s) -
Wahed Abdus S.,
Luong The Minh,
Jeong JongHyeon
Publication year - 2009
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.3598
Subject(s) - weibull distribution , exponentiated weibull distribution , statistics , generalization , cumulative distribution function , parametric statistics , weibull modulus , mathematics , parametric model , computer science , econometrics , probability density function , mathematical analysis
In this article, we propose a new generalization of the Weibull distribution, which incorporates the exponentiated Weibull distribution introduced by Mudholkar and Srivastava ( IEEE Trans. Reliab. 1993; 42 :299–302) as a special case. We refer to the new family of distributions as the beta‐Weibull distribution. We investigate the potential usefulness of the beta‐Weibull distribution for modeling censored survival data from biomedical studies. Several other generalizations of the standard two‐parameter Weibull distribution are compared with regards to maximum likelihood inference of the cumulative incidence function, under the setting of competing risks. These Weibull‐based parametric models are fit to a breast cancer data set from the National Surgical Adjuvant Breast and Bowel Project. In terms of statistical significance of the treatment effect and model adequacy, all generalized models lead to similar conclusions, suggesting that the beta‐Weibull family is a reasonable candidate for modeling survival data. Copyright © 2009 John Wiley & Sons, Ltd.