Identifying Best-Fit Probability Distribution for Modelling Annual Maximum Daily Rainfall

Abstract

The study examines the annual maximum daily rainfall (AMDR) in Multan, Pakistan, using data from 1951 to 2016. L-Moments (LM), Maximum Likelihood Estimation (MLE), Maximum Product of Spacings (MPS), and Bayesian estimation were the estimation techniques used to estimate the parameters of Pearson Type-III, Gumbel, Weibull, and Generalized Extreme Value (GEV) probability distributions. The models were evaluated using different accuracy measures. Based on the comparative results using accuracy metrics, the Weibull distribution appears to best fit the rainfall data for Multan. Among the parameter estimation methods for the Weibull distribution, MPS performs better than other methods. The identification of the Weibull distribution as best-fit probability model makes it more appropriate for modelling rainfall data and hence planning for water resources, agriculture, and disaster risk reduction in Multan and infrastructure design and flood risk management.