A Comparative Analysis of Estimation Methods for Pearson Type 3 Distribution Using Rainfall Extremes

Abstract

Selecting an appropriate model and method of estimation is critical for precise parameter estimation, accurate representation, and reliable prediction in hydrological and extreme rainfall analysis. This study investigates the application of the Pearson Type III (PE3) distribution for extreme rainfall analysis on Annual Maximum Rainfall Series (AMRS) in Zone B of Pakistan which includes sites of upper Punjab, KPK and Kashmir according to PMD. Three parameter estimation methods Maximum Product of Spacings (MPS), Lmoments (LM), and Maximum Likelihood Estimation (MLE) are evaluated for their efficiency in fitting the PE3 distribution to the extreme rainfall data. The superior performance of MPS is attributed to its ability to minimum value of RMSE and Bias almost in all stations of zone B for moderate sample size and where skewness and kurtosis is moderate to high and provide better estimates for the tail behavior of the distribution. The findings underscore the potential of the MPS method as a reliable estimation method for Pearson Type 3 distribution.