Nonparametric Erlang Mixtures

Music City Center 

Erlang mixture models are essential tools for modeling insurance losses and evaluating aggregated risk measures. However, finding the maximum likelihood estimate (MLE) of Erlang mixtures is challenging due to the discrete nature of the parameter space for shape. This discreteness complicates the application of the standard expectation-maximization (EM) algorithm, which is commonly used in mixture models. Although alternative algorithms have been proposed to compute the MLE of Erlang mixtures, they are often restricted to parametric models and tend to converge to local maxima of the likelihood function. In this study, we focus on the nonparametric Erlang mixture model which offers greater flexibility compared to parametric models, and introduce an algorithm to estimate the nonparametric maximum likelihood estimate (NPMLE) of Erlang mixtures. By exploiting the gradient function, this method efficiently identifies critical support points, enhancing the likelihood of finding the global maximizer. Numerical studies demonstrate that our approach provides more stable and accurate performance in estimating the MLE for Erlang mixture models compared to existing methods.

Erlang mixtures

nonparametric mixtures

NPMLE

gradient function

EM algorithm 

Korean International Statistical Society