Analyzing the Best Fitted Probabilistic Model for the Seasonal Rainfall Data in Khulna Region of Bangladesh

Abstract

There are several pieces of research on the statistical modeling of rainfall data in Bangladesh. Since all the seasons of a year do not receive a similar amount of rainfall, hence one single statistical model might not be able to explain the pattern of rainfall at any season of a year. According to the climatologists, Bangladesh has four seasons which are Monsoon, Post-monsoon, Summer, and Winter based on the geographical characteristics of this country. This paper aims to determine the best-fitted probability distribution model for the monthly rainfall data of each particular season in the Khulna district of Bangladesh using the rainfall data of the Khulna region from 1951 to 2018. Very commonly used seven continuous distributions- Normal, Weibull, Gamma, Log-normal, Exponential, Cauchy, and Logistic distributions were used to model the data and to evaluate the performances of the distributions, three non-parametric goodness-of-fit tests were conducted, and AIC, BIC values were calculated. Parameters of the distributions were estimated by the maximum likelihood method. The best-fit result of each season was taken as the distribution with the lowest AIC and BIC values. Among the seven distributions, the Gamma distribution showed the best-fit results of the monthly rainfall data for the Monsoon, Post-Monsoon, and Winter Season, and the Weibull distribution showed the best-fit result for Summer Season.