Mixed log series geometric distribution for sequences of dry days

Abstract

The development of rainfall occurrence models is continuously being explored by a number of researchers in the field since the 20th century. In order to further enhance the development of rainfall occurrence modeling, this present study is aimed to propose a new probability model which is able to describe the daily series of rainfall occurrence, particularly on the duration of consecutive dry or wet days in Peninsular Malaysia. In selecting the most successful model to describe the distribution of the rainfall event, the model with the less number of parameters is preferred. In addition, there have been cases where the model with more parameters did not show a significant fit. In this situation, it is necessary to develop a more appropriate model which can be used for data generation purposes and other applications. Based on several probability models developed previously, the mixture of log series with geometric distribution (MLGD) is proposed as the alternative probability model to describe the distribution of dry (wet) spells in daily rainfall events. This study aims to fit nine types of probability models including the MLGD to dry spells data for 16 selected rainfall stations in Peninsular Malaysia. The sequence of dry days will be analyzed separately at each station using daily rainfall observations for the period of 1975 to 2004. The adequacy of the MLGD and the existing probability models in fitting the observed distribution of dry spells at each station are evaluated using a chi square goodness-of-fit test. The results demonstrated that all the data sets were found to successfully fit the new proposed model, the MLGD, in representing the sequence of dry days over the peninsula. Moreover, this model was also found to best fit the three data sets which were not able to fit the existing models.