A Variational Bayesian Approach for Estimating Parameters of a Mixture of Erlang Distribution

Abstract

This article proposes a fast algorithm for estimating parameters of a mixture of Erlang (MER) distribution from empirical samples. In particular, we develop a variational approach for approximately computing posterior distributions of parameters of MER distribution in the Bayesian context. Computation speed of the proposed method becomes up to 200 times faster than that of the Markov chain Monte Carlo (MCMC) method. The estimates of proposed method are almost same as those of MCMC method. Moreover, we discuss how to estimate shape parameters of Erlang distribution based on a certain goodness-of-fit criterion in the proposed variational Bayes method.

Keywords:

• Bayesian statistics
• Mixture of Erlang distributions
• Variational Bayes

Mathematics Subject Classification:

• 62F15
• 62E17

Notes

In the strict sense, the variational posterior (density) needs to be denoted by q(· | 𝒟). For the sake of simplicity, however, we omit the conditioning on the observed data 𝒟.

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