A Three-Parameter Alpha Power Erlang Distribution for Modeling Lifetime Data

Abstract

The alpha power family of distributions introduces a new type of distribution by adding an extra parameter to its baseline distribution, making it highly suitable for lifetime data analysis. In this paper, we propose the three-parameter alpha power Erlang (APEr) distribution, where the baseline Erlang distribution is composed of the sum of multiple exponential distributions and is a special case of the gamma distribution. After defining the probability density and cumulative distribution functions of the APEr distribution, we present its theoretical properties, including quantiles, moments, and maximum likelihood estimation (MLE) of its parameters.Furthermore, using a simulation study, we verify the consistency of the parameter estimators and demonstrate the improvement in inference quality with increasing sample size. Finally, we compare the performance of the proposed distribution in fitting on two real-world datasets against the alpha power exponential, exponential, and Erlang distributions, demonstrating its superiority in these applications.