Extreme Values and Reliability Measures of Continuous Erlang Mixtures
Beatrice M. Gathongo *
Mathematics Department, University of Nairobi, Kenya.
Esther N. Irungu
Mathematics Department, University of Nairobi, Kenya.
*Author to whom correspondence should be addressed.
Abstract
This study delves into Extreme Value Theory, focusing on the limiting distributions of continuous Erlang mixtures and their mixing distributions. It categorizes Erlang mixtures based on their extreme value types, demonstrating that the limiting distributions of the Erlang mixtures can be either Type I (Gumbel) or Type II (Frechet), contingent on the mixing distribution. Further, this study derives the mean residual lifetime and equilibrium distributions of these mixed distributions.
Keywords: Extreme value theory, limiting distribution, Erlang mixture, mean residual lifetime distribution, equilibrium distribution, mixing distribution, mixed distribution