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.
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