Performance Comparison of Methods in Estimating Zero-Inflated Weibull Parameters for Fitting Monthly Precipitation of Nan Region Thailand
Tanachot Chaito (a*), Manad Khamkong (a,b)
a) Department of Statistics, Faculty of Science, Chiang Mai University, Chiang Mai 50200,Thailand
*tanachot.boy[at]gmail.com
b) Data Science Research Center, Department of Statistics, Faculty of Science, Chiang Mai University, Chiang Mai 50200,Thailand
Abstract
The objective of this research is to compare methods of parameter estimation for a zero inflated Weibull distribution (ZIW). The methods used to estimate parameters include the maximum likelihood estimation (MLE), the expectation maximization (EM) algorithm and the percentile estimation (PE). The results of a simulation study; the MLE and EM methods gave small mean square error (MSE) values and both methods are effective in estimating parameters which are not different while the PE method (using the 25th and 75th) had small average relative bias (AvRB) values when sample size and shape parameters increase. Therefore, the MLE and EM methods were the best parameter estimation method for a ZIW distribution. In this research the monthly rainfall data from two rain gauging stations at Pua and Mueang, Nan, Thailand during the period of 1960 to 2017 were used in this study. The goodness of fit test of monthly rainfall data from two stations found that a ZIW distribution was the most appropriate. Moreover, when we analyzed the tendency of drought, Mueang station had no tendency for drought but Pua station had a rain trend.
Keywords: Expectation Maximization algorithm; Maximum Likelihood estimation; percentile estimation; rainfall data
Topic: Applied Mathematics and statistics