The Compound Family of Generalized Inverse Weibull Power Series Distributions

Abstract

Compounding a continuous lifetime distribution with a discrete one is a useful technique for constructing flexible distributions to facilitate better modeling of lifetime data. In this paper, a new family of lifetime distributions, called the generalized inverse Weibull power series distribution is introduced. This new family is obtained by compounding the generalized inverse Weibull and truncated power series distributions. This compounding procedure follows the same way that was previously carried out by [1]. This family contains several new distributions such as generalized inverse Weibull Poisson; inverse Weibull Poisson; inverse Rayleigh Poisson; inverse exponential Poisson; generalized inverse Weibull logarithmic; inverse Weibull logarithmic; inverse Rayleigh logarithmic; inverse exponential logarithmic; generalized inverse Weibull geometric; inverse Weibull geometric; inverse Rayleigh geometric  and inverse exponential geometric as special cases. The hazard rate function of the new family of distributions can be increasing, decreasing and bathtub-shaped. Several properties of the new family including; quantile, entropy, moments and distribution of order statistics are provided. The model parameters of the new family are estimated by the maximum likelihood method. The two new models namely; generalized inverse Weibull Poisson and the generalized inverse Weibull geometric distributions are studied in some details. Finally, applications to two real data sets are analyzed to illustrate the flexibility and potentiality of the new family.