Fitting Statistical Distributions to Rainfall Data with Different Estimation Techniques: An Empirical Study from Pabna and Dinajpur Districts

Abstract

Bangladesh is a country of diverse climatic conditions because of its rainfall and other geographical conditions which have a complex impact on economic and social aspects. The statistical distributions are used in many real life data for modeling and predicting. Knowing the real distribution of rainfall rather than depending on basic summary statistics would improve many uses of rainfall data. The aim of this paper is twofold: first, the performance of different statistical distributions such as Normal, Log-Normal, Gamma Weibull, and Gumbel are compared for modeling the monthly rainfall data from Pabna and Dinajpur districts from January 1971 to December 2015; second, the performance of the Maximum Likelihood Estimation (MLE), Quantile Matching Estimation (QME), and the Maximum Spacing Estimation are also compared for fitting these statistical distributions. The empirical study showed that Gamma distribution performs better for fitting the monthly rainfall data for both Pabna and Dinajpur districts of the three methods like Maximum Likelihood Estimation (MLE) method, the Quantile Matching Estimation (QME), and the Maximum Spacing Estimation (MSE) method. The Normal distribution performs worse of these study areas. By the comparison of these three methods we found that Maximum Likelihood Estimation (MLE) gives better results. This study provides the actual distribution of rainfall data of these study areas.

International Journal of Statistical Sciences, Vol. 23(2), November, 2023, pp 87-106