Generalized extended Marshall-Olkin family of lifetime distributions

We introduce a new generalized family of nonnegative continuous distributions by adding two extra parameters to a lifetime distribution, called the baseline distribution, by twice compounding a power series distribution. The new family, called the lifetime power series-power series family, has a serial arrangement of parallel structures, which extends the Marshall and Olkin structure. Four special models are discussed. A mathematical treatment of the new distributions is provided, including ordinary and incomplete moments, quantile, moment generating and mean residual functions. The maximum likelihood estimation technique is used to estimate the model parameters and a simulation study is conducted to investigate the performance of the maximum likelihood estimates. Its applicability is also illustrated by means of two real data sets.