Parameter Estimation of Weighted Erlang Distribution Using R Software

Abstract

The Erlang distribution belongs to a group of continuous probability distributions with universal relevance primarily due to its relation to the exponential and Gamma distributions. If the time period of individual telephone calls is exponentially distributed, then the duration of the successive calls follows the Erlang distribution. In this paper, we take into account the weighted version of Erlang distribution known as weighted Erlang distribution. We obtain the posterior mean and posterior variance of the model. Maximum likelihood method of estimation is discussed. Bayes estimates of the scale parameter of Weighted Erlang distribution is offered for consideration under Squared Error Loss Function (SELF), Quadratic Loss Function (QLF) and entropy Loss Function (ELF) using Jeffrey`s, extension of Jeffrey`s and Quasi priors.

Keywords: Erlang distribution, Weighted Erlang distribution, Loss function, Bayesian estimation.