A Lifetime Distribution Based on a Transformation of a Two-Sided Power Variate

Abstract

We introduce a new generalization of Weibull distribution by making use of a transformation of the standard two- sided power distributed random variable. Weibull and the exponentiated Weibull distributions are submodels of this new distribution.We show that this newly defined distribution is in fact a mixture of the truncated forms of Weibull and the exponentiated Weibull distributions. The new distribution has two shape parameters that make it more flexible for modeling data than Weibull and exponentiated Weibull distributions. We study its properties, consider the maximum likelihood estimation procedure and apply it on some real data sets from reliability.

Keywords

• generalized Weibull distribution; maximum likelihood estimation; mixture distribution; reliability; two-sided power distribution