Fitting Distributions to the Annual Maximum Rainfall in Punjab and Azad Jammu and Kashmir

Abstract

This study analyzed the fit of two-parameter Frechet, Weibull, log-logistic, and gamma distributions to annual maximum rainfall in eight different Punjab and Azad Kashmir sites, from 1980-2015. The maximum likelihood, Moments, Bayesian and probability-weighted moment methods are used to estimate parameters, and the Kolmogrove Simirnove has been applied for the goodness of fit criterion. Based on scores of the goodness of fit test the candidate distributions are found to be the best fit for annual maximum rainfall data for selected sites of Punjab and Azad Jammu and Kashmir, except for Frechet distribution the Moment estimators for Lahore, Islamabad, and Sialkot site and Probability weighted moments for Miawali are not found good. Moreover, rainfall quantiles with the best-fitted method (for many return periods) of each site have been estimated using the quantile functions of the candidate distributions for future prediction.