Optimal parameter estimation for zero-inflated gamma distributions with application to rainfall data of Yom River in Northern Thailand

Abstract

© 2017 Author(s). In this study, the application of the Expectation Maximization (EM) algorithm for parameters estimation of a Zero - Inflated Gamma Distribution (ZIG) is of interest in which we were used several experiments in the simulation. Maximum likelihood estimation (MLE) and moment methods were estimated parameters to determine the best parameter estimation method for a ZIG distribution. By examining minimal mean square error (MSE) and average relative bias (AvRB) values of the test, it was found that the EM algorithm and MLE were the best parameter estimation method for ZIG distribution when the sample size was small, but, the EM algorithm was the best parameter estimation method when the sample size was large. The moment method was suitable for some parameter since its MSE and AvRB value was very high. In order to test for weather, the rainfall data in the summer season from Yom River in Northern Thailand follows a ZIG distribution using the three estimation methods, it was found that the estimated parameter values using MLE and EM algorithm were similar. Furthermore, we analyzed drought trends of all. We found that no tendency towards drought was detected.