A compound class of Weibull and power series distributions

In this paper we introduce the class Weibull power series (WPS) of distributions which is obtained by compounding Weibull and power series distributions, where compounding procedure follows same way that was previously carried out by Adamidis and Loukas (1998). This new class of distributions has as particular case the two-parameter class exponential power series (EPS) of distributions, which was introduced recently by Chahkandi and Ganjali (2009). Like EPS distributions, our class contains several distributions which have been introduced and studied such as: exponential geometric (Adamidis and Loukas, 1998), exponential Poisson (Kus, 2007) and exponential logarithmic (Tahmasbi and Rezaei, 2008) distributions. Moreover, the hazard function of our class may take increasing, decreasing, upside down bathtub forms, among others, while hazard function of a EPS distribution is only decreasing. We obtain several properties of the WPS distributions such as moments, order statistics, estimation by maximum likelihood and inference for large sample. Furthermore, EM algorithm is also used to determine the maximum likelihood estimates of the parameters and we discuss maximum entropy characterizations under suitable constraints. Special distributions are studied in some details. Applications to real data sets are given to show the flexibility and potentiality of the proposed class of distributions. ∗Corresponding author. Email: [email protected]