Geometric distributions MinMax and MaxMin modified as lifetime distributions and statistical estimators for them

Abstract

In the current work, two new dynamic models were introduced that target the serial-parallel and parallel-serial type networks for which the lifetimes of the units are geometrically distributed random variables. Calculation formulas were derived for the cumulative distribution functions of their lifetimes, but also of their survival/reliability and hazard functions. Maximum likelihood estimators were derived for this lifetime distributions. The results are illustrated by separate examples.