The Complementary Exponentiated Inverted Weibull Power Series Family of Distributions and its Applications
Amal S. Hassan
Institute of Statistical Studies and Research, Cairo University, Egypt.
A. M. Abd-Elfattah
Institute of Statistical Studies and Research, Cairo University, Egypt.
Asmaa H. Mokhtar *
Institute of Statistical Studies and Research, Cairo University, Egypt.
*Author to whom correspondence should be addressed.
Abstract
In statistical literature, several distributions are used to model lifetime data. But many –if not most– of these distributions lack of certain lifetime context motivation. Recently, attempts have been made to define new families of probability distributions that extended well known families of distributions and at the same time offer great flexibility in a real data modeling. In this paper, a new family of distributions is introduced by compounding exponentiated inverted Weibull and power series distributions. The properties of the new family are discussed, including quantiles, moments and moment generating function. The estimation of the model parameters is performed by the maximum likelihood method. The new family generalizes some new lifetime distributions. In particular, two special models belonging to this family are studied in some details. Applications to real data sets are given to show the flexibility and potentiality of the proposed family of distributions.
Keywords: Exponentiated inverted Weibull distribution, power series distribution, order statistics, hazard function.