Generalized extended Marshall-Olkin family of lifetime distributions

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