Fitting daily rainfall amount in Malaysia using the normal transform distribution

Abstract

This research presents a statistical study of rainfall which compares several types of normal transform distributions that describe rainfall distribution in Malaysia over a multi-year period. The normal transform distribution meaning that all tested distributions were established based on some modification or transformation of the normal distribution through several methods. The lognormal, skew normal and mixed lognormal distributions are among the normal transform distributions that are proposed and tested to identify the optimal model for daily rainfall amount in several rain gauge stations in Malaysia. The selected model will be chosen based on the minimum error produced by seven criteria of goodness of-fit (GOF) tests, namely the median of absolute difference (MAD) between the empirical and hypothesized distribution function, the traditional Empirical Distribution Function (EDF) Statistics which include Kolmogorov-Smirnov statistic D, Anderson Darling statistic A2 and Cramer-von-Mises statistic W2 and the new method of EDF Statistics based on the likelihood ratio statistics. Of the three models tested, the mixed lognormal is found to be the most appropriate distribution for describing the daily rainfall amount in Malaysia.