Modelling monthly rainfall in Peninsular Malaysia using tweedie distribution

Abstract

This study focused on modelling rainfall process by using Generalised Linear Model (GLM) when the response variable follows a distribution that comes from Tweedie family of distributions. The Tweedie family belong to the class of exponential dispersion models where the variance is proportional to some power of the mean. A special case of power-variance family of distributions, called the Tweedie distribution is used to handle the continuous real data with a discrete mass at zero. These distributions has been previously used to enable a single model for rainfall to be produced. In this context, the present study applied the Tweedie family of distributions to fit the monthly rainfall data from 10 selected rain gauge stations in Peninsular Malaysia which covers the period from January, 1980 to December, 2015. The aim of this study is to determine whether the distributions within the Tweedie family fit well the monthly Malaysian rainfall series. First, the possibility that different distributions are needed for each station was explored by estimating the index parameter, ??. To do so, the profile likelihood plot is used to estimate the ?? index for which the log-likelihood is maximized and hence the appropriate distribution within the Tweedie family was identified. Within the Tweedie family, the Tweedie distribution was found appropriate to model both rainfall occurrence and rainfall amount simultaneously. Then, Tweedie GLM with sine and cosine functions of different harmonics are used to account for cyclical rainfall pattern. The results indicated that the stations in the eastern region are best described with one harmonics while two harmonics are required for the stations in the west and northwest region. The plots of the predicted mean monthly rainfall from the simulated data shows a resemblance to that of the observed data. Finally, reparameterization of Tweedie parameters was adopted and found to predict the amount of rain per rainfall event and probability of zero rainfall well for all months. The model provide a good description and useful information for describing the cyclical nature of rainfall pattern in the studied stations.