Mixed probability models for dry and wet spells

When identifying the best model for representing the behavior of rainfall distribution based on a sequence of dry (wet) days, focus is usually given on the fitted model with the least number of estimated parameters. If the model with lesser number of parameters is found not adequate for describing a particular data distribution, the model with a higher number of parameters is recommended. Based on several probability models developed by previous researchers in this field, we propose five types of mixed probability models as the alternative to describe the distribution of dry (wet) spells for daily rainfall events. The mixed probability models comprise of the combination of log series distribution with three other types of models, which are Poisson distribution (MLPD), truncated Poisson distribution (MLTPD), and geometric distribution (MLGD). In addition, the combination of the two log series distributions (MLSD) and the mixed geometric with the truncated Poisson distribution (MGTPD) are also introduced as the alternative models. Daily rainfall data from 14 selected rainfall stations in Peninsular Malaysia for the periods of 1975 to 2004 were used in this present study. When selecting the best probability model to describe the observed distribution of dry (wet) spells, the Akaike’s Information Criterion (AIC) was considered. The results revealed that MLGD was the best probability model to represent the distribution of dry spells over the Peninsular.