Statistical Modelling 6 (2006), 265277
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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