Some Generalized Families of Weibull Distribution: Properties and Applications

Abstract

The Weibull distribution has been applied in various fields, especially to fit life time data. Some of these applications are limited partly due to the fact that the distribution has monotonically increasing, monotonically decreasing or constant hazard rate. This limitation undoubtedly inspired researchers to develop generalized Weibull distribution that can exhibit unimodal or bathtub hazard rate. In this article, we introduce six new families of T-Weibull{Y} distributions arising from the quantile function of a random variable Y. These six families are: The T-Weibull{uniform}, T-Weibull{exponential}, T-Weibull{log-logistic}, T-Weibull{Fré chet}, T-Weibull{logistic} and T-Weibull{extreme value}. Some properties of these families are discussed and general expressions for the quantile function, the Shannon's entropy, the non-central moments and the mean deviations are provided. Different new members of the T-Weibull{Y} families are derived and some of their properties are discussed. Two real data sets are used to illustrate the potential usefulness of the T-Weibull{Y} distributions and the results are compared with the results from some existing distributions.