Intercomparison of Estimators of Gumbel Distribution using Goodness-of-Fit Tests for Estimation of Extreme Rainfall
Keywords:
Anderson–Darling test, Extreme Value Analysis, Gumbel distribution, Kolmogorov Smirnov test, Mean Absolute Percentage Error, Probability Weighted Moments, RainfallAbstract
Estimation of extreme rainfall for a given return period is of utmost importance for planning, design and management of hydraulic structures and riverfront development projects. This can be achieved through Extreme Value Analysis (EVA) that involves fitting of Gumbel probability distribution to the series of Annual 1-day Maximum Rainfall (AMR). Standard parameter estimation procedures such as Method of Moments (MoM), Maximum Likelihood Method (MLM) and Probability Weighted Moments (PWM) are applied for determination of parameters of the Gumbel distribution. This paper presents a study on comparison of MoM, MLM and PWM estimators of Gumbel distribution adopted in EVA of rainfall for Kalyan, Thane and Ulhasnagar sites of Ulhas river basin. Goodness-of-Fit tests viz., Anderson–Darling, Kolmogorov–Smirnov and Mean Absolute Percentage Error are used for checking the adequacy of fitting of three methods of Gumbel probability distribution to the AMR data. Based on the GoF tests results, the MLM is identified as better-suited method amongst three methods applied for determination of parameters of Gumbel distribution for estimation of extreme rainfall at Kalyan, Thane and Ulhasnagar sites
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