Statistical Modelling and Best-Fit Distribution Analysis of Annual Rainfall in the Bundelkhand Region, Madhya Pradesh, India

Abstract

This study analyzes time series data on annual rainfall from 2008–2009 to 2021–2022 for the Bundelkhand region of Madhya Pradesh, encompassing the districts of Chhatarpur, Tikamgarh, Damoh, Sagar, Datia, and Panna. It evaluates the suitability of various statistical distribution models to represent the annual rainfall data across these six districts. Utilizing a combination of model selection criteria, including Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), along with multiple goodness-of-fit tests (Kolmogorov–Smirnov, Cramér–von Mises, and Anderson–Darling), the research assesses the fit of four probability distributions: Normal, Log-Normal, Gamma, and Weibull. Results indicate that the Log-Normal distribution most accurately models rainfall data in Damoh, Panna, Sagar, and Tikamgarh districts, effectively capturing the characteristic positive skewness of hydrological data. The Gamma distribution is identified as the best fit for the Datia region, while the Weibull distribution provides the best model for Chhatarpur. In all cases, the Normal distribution is consistently outperformed by the other three due to its inability to capture extreme values and data skewness. These insights highlight the importance of selecting suitable statistical models for reliable hydrological analysis, risk assessment, and climate studies in the Bundelkhand region.