Some classes of statistical distributions. Properties and Applications

We propose a new method of constructing statistical models which can be interpreted as the lifetime distributions of series-parallel/parallel- series systems used in characterizing coherent systems. An open problem regarding coherent systems is comparing the expected system lifetimes. Using these models, we discuss and establish conditions for ordering of expected system lifetimes of complex series-parallel/parallel-series systems. Also, we consider parameter estimation and the analysis of two real data sets. We give formulae for the reliability, hazard rate and mean hazard rate functions.