Optimizing Quantiles Estimation of Annual Maximum Rainfall in Pakistan Considering Pearson Type-III Distribution with Different Methods of Estimation

Abstract

Particularly considering the rapidly intensifying effects of global climate change, extreme rainfall events provide challenging obstacles to the effective management of water resources and the advancement of infrastructure. It is becoming increasingly important to precisely anticipate these events as Pakistan struggles with growing vulnerabilities to more intense extreme weather events, such as the devastating floods of 2010 and 2022. To assess extreme rainfall occurrences in Pakistan, this study examines the effectiveness of the Maximum Product Spacing (MPS) approach in conjunction with the Pearson Type III distribution. This research tries to improve the accuracy and dependability of extreme rainfall models by examining MPS with other estimating techniques. Pakistan is at the forefront of the effects of climate change, with increasing susceptibilities to more intense extreme weather events. The study examines differences in the annual maximum rainfall series in the Pakistan Meteorological Department demarcated zones A and C within this framework. The study concluded that when the data shows minor to moderate skewness and kurtosis and when the samples are small, the estimates produced by the LM approach show little Bias. When there is significant skewness and kurtosis in the data and a small to moderate sample size, the MPS approach is an acceptable substitute that yields accurate estimates. When data from characteristic values are low, and sample sizes are big, the MLE approach offers benefits. The superior performance of MPS is attributed to its ability to minimum the value of RMSE and Bias in all stations of zone A and C. It provides better estimates for the behavior of the tail of the distribution, which is significant for extreme value analysis. These findings provide useful guidance that the MPS method is reliable when fitted with the PE3 distribution, especially for extreme values.