Rainfall Frequency Analysis Using Frechet and Log-Logistic Distributions of Sites of Azad Jammu and Kashmir, Pakistan

Abstract

The paper illustrates the application of at-site frequency analysis using relatively nontraditional probability distributions adopting four methods of parameter estimation using annual maximum rainfall series (AMRS) (from 1980 to 2015) of three sites; Muzaffarabad, Garhi Dupatta and Kotli of Azad Jammu and Kashmir, Pakistan. Critical assumptions related to AMRS for frequency analysis have been validated through run test (to check the randomness of AMRS at each site) and Mann Whitney test (to check the distribution of AMRS at given sites as identical or not). Two probability distributions; Frechet and Log-logistic have been used as candidate distributions to model AMRS at given sites. The parameters of these distributions have been estimated using four methods; Probability Weighted Moments Estimation (PWME), Maximum Likelihood Estimation (MLE), Bayesian Estimation (BE) and Moments Estimation (ME) methods. The Kolmogorov Smirnov test has been used as goodnessof-fit criteria. The results show suitability of the selected probability distributions for the observed AMRS series at given sites with BE and MLE methods as adequate for estimation. Moreover, the results indicate that ME method is not a preferred choice for the estimation of parameters and quantiles for various return periods.