Methods for Testing the Rainfall Dispersion Data Fitted to a Gamma Distribution of Songkhla, Thailand
Keywords:
Measure of dispersion, Power of the test, Skewed distribution, Test statistics, Type I error rateAbstract
Floods are ordinary natural disasters in Songkhla, Thailand that occur almost every year due to heavy rainfall during the rainy season. The organizations related to agriculture and water resource planning can solve or reduce the flood problem in Songkhla by testing the monthly rainfall dispersion for flood monitoring. We can use the coefficient of variation (CV) to measure the dispersion of rainfall amount in different areas because the rainfall amount varies greatly depending on the region and season. The objective of this study is to propose two methods for testing the CV for a gamma distribution. The methods based on Score-type and Wald-type confidence intervals were applied for testing the monthly rainfall dispersion which these data were well-fitted with a gamma distribution. Using Monte Carlo simulations, the type I error rate and power of the test for two test statistics were estimated under several shape parameter values in a gamma distribution. The simulation results indicated that the test statistic based on Wald-type confidence interval performed better than its competitor in terms of the attained nominal significance level (0.05). The mean of the absolute differences between the empirical type I error rates and 0.05 for those based on Score-type and Wald-type confidence intervals was 0.0480 and 0.0067, respectively. Therefore, the test statistic based on Wald-type confidence interval is recommended for analysis in similar scenarios. Both test statistics were utilized to test the rainfall dispersion data from Sa Dao Meteorological Station in Songkhla. The study concluded that the population CV of the Songkhla’s rainfall was not significantly different from the hypothesized setting of 0.90.
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