Fitting the statistical distribution for daily rainfall in Peninsular Malaysia based on AIC criterion

Abstract

This paper presents several types of exponential distributions to describe rainfall distribution in Peninsular Malaysia over a multi-year period. The exponential, gamma, mixed exponential and mixed gamma distributions are compared to identify the optimal model for daily rainfall amount based on data recorded at rain gauges stations in Peninsular Malaysia. The models are evaluated based on the Akaike Information criterion (AIC). The log likelihood ratio test has been employed to determine whether the differences in AIC between tested models are statistically significant. However, this test is restricted by the need of the models to be nested. Since the gamma is not nested in the mixed exponential model so comparison has been done indirectly using the mixed gamma as the nested model. Overall, this study has shown that the mixture of two distributions is better than single distributions for describing the daily rainfall amount in Peninsular Malaysia based on the AIC criterion and their differences in AIC are statistically significant