Statistical Modelling 6 (2006), 265–277

Generalization of the Weibull distribution: the odd Weibull family

Kahadawala Cooray
Department of Mathematical Sciences,
University of Nevada,
Las Vegas, NV 89154
USA.
eMail: coorayk@unlv.nevada.edu

Abstract:

Abstract: A three-parameter generalization of the Weibull distribution is presented to deal with general situations in modeling survival process with various shapes in the hazard function.This generalizedWeibull distribution will be referred to as the oddWeibull family, as it is derived by considering the distributions of the odds of theWeibull and inverseWeibull families. As a result, the oddWeibull family is not only useful for testing goodness-of-fit of the Weibull and inverse Weibull as submodels, but it is also convenient for modeling and fitting different data sets, especially in the presence of censoring. The model parameters for uncensored data are estimated in two different ways because of the fact that the inverse transformation of the odd Weibull family does not change its density function. Adequacy of the model for the given uncensored data is illustrated by using the plot of scaled fitted total time on test (TTT) transforms. Furthermore, simulation studies are conducted to measure the discrepancy between empirical and fitted TTT transforms by using a previously proposed test statistic. Three different examples are, respectively, provided based on data from survival, reliability and environmental sciences to illustrate increasing, bathtub and unimodal failure rates.

Keywords:

confidence band; goodness-of-fit; maximum likelihood; total time on test transform

Downloads:

Example data in zipped archive


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