ORIGINAL PAPER Fitting the distribution of dry and wet spells with alternative probability models Sayang Mohd Deni Æ Abdul Aziz Jemain Received: 21 September 2007 / Accepted: 16 October 2008 / Published online: 14 November 2008 Ó Springer-Verlag 2008 Abstract The development of the rainfall occurrence model is greatly important not only for data-generation purposes, but also in providing informative resources for future advancements in water-related sectors, such as water resource management and the hydrological and agricultural sectors. Various kinds of probability models had been introduced to a sequence of dry (wet) days by previous researchers in the field. Based on the probability models developed previously, the present study is aimed to propose three types of mixture distributions, namely, the mixture of two log series distributions (LSD), the mixture of the log series Poisson distribution (MLPD), and the mixture of the log series and geometric distributions (MLGD), as the alternative probability models to describe the distribution of dry (wet) spells in daily rainfall events. In order to test the performance of the proposed new models with the other nine existing probability models, 54 data sets which had been published by several authors were reanalyzed in this study. Also, the new data sets of daily observations from the six selected rainfall stations in Peninsular Malaysia for the period 1975–2004 were used. In determining the best fitting distribution to describe the observed distribution of dry (wet) spells, a Chi-square goodness-of-fit test was considered. The results revealed that the new method proposed that MLGD and MLPD showed a better fit as more than half of the data sets successfully fitted the dis- tribution of dry and wet spells. However, the existing models, such as the truncated negative binomial and the modified LSD, were also among the successful probability models to represent the sequence of dry (wet) days in daily rainfall occurrence. 1 Introduction The development of a rainfall occurrence model is increasingly in demand, not only for data-generation pur- poses, but also to provide some useful information in various applications, including water resource management and the hydrological and agricultural sectors. Identifying the appropriate model of daily rainfall occurrence, partic- ularly on the distribution of dry (wet) spells, is very important as almost all of the climate variables are dependent on the rainfall events. The study on daily rainfall occurrence models, partic- ularly on the distribution of the dry (wet) spells, has been explored by many researchers since the early part of the 20th century. Several probability models which have been applied for the distribution of dry (wet) spells were introduced in the literature by previous researchers, such as the log series distribution (LSD) by Williams (1952), geometric distribution (GD) by Gabriel and Neumann (1957), modified log series distribution (MLD) by Green (1970), compound geometric distribution (CGD) by Yap (1973), Polya distribution (PLD) by Brooks and Carruthers (1953), truncated negative binomial distribution (TNBD) by Buishand (1978), and mixed geometric series S. M. Deni (&) Center for Statistical Studies, Faculty of Information Technology and Quantitative Science, Universiti Teknologi MARA (UiTM), 40450 Shah Alam, Selangor, Malaysia e-mail: sayan929@salam.uitm.edu.my A. A. Jemain School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia (UKM), 43600 Bangi, Selangor, Malaysia e-mail: azizj@ukm.my 123 Meteorol Atmos Phys (2009) 104:13–27 DOI 10.1007/s00703-008-0010-7