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THE MIXTURE WEIBULL-GENERALIZED GAMMA DISTRIBUTION

The mixture distribution is defined as one of the most important ways to obtain new probability distributions in applied probability and several research areas. It is a compounding of statistical distributions, which arises when sampling is from inhomogeneous populations (or mixed populations) with a different probability density function in each component. Finite mixture models also play a vital role in life testing and reliability. According to the previous reasons, we have been looking for more flexible alternative to the lifetime data. This paper introduces a new mixed distribution, namely the Mixture Weibull-Generalized Gamma distribution, which is obtained by M. S. Hamed 140 mixing Weibull and generalized gamma distributions. We refer to the new distribution as (W-GG) distribution. The new model contains twenty eight lifetime distributions as special cases such as the Weibull, Lindley, Quasi Lindley, Janardan, Gamma, Rayleigh and exponential distributions, among others. The properties of the W-GG distribution are discussed and the maximum likelihood estimation is used to evaluate the parameters. Explicit expressions are derived for the moments and examine the order statistics. This model is capable of modeling various shapes of aging and failure criteria.