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 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.