Assessing Adequacy of Probability Distribution for Modelling Annual Maximum Rainfall

N. Vivekanandan


Estimation of rainfall for a desired return period is one of the pre-requisites for any design purposes at a particular
site, which can be achieved by probabilistic approach. This paper exemplifies the use of 2-parameter distributions
such as Extreme Value Type-1, Gamma and Log Normal-2; and 3-parameter distributions such as Log Normal-3,
Pearson Type-3 (P3) and Log Pearson Type-3 for modelling Annual Maximum Rainfall (AMR) data observed at
Visakhapatnam, Yetikoppaka and Devarapalli rain-gauge stations. Maximum likelihood method is used for
determination of distributional parameters for modelling AMR. Goodness-of-Fit (GoF) tests such as Chi-square and
Kolmogorov-Smirnov are applied for checking the adequacy of fitting of distributions for modelling AMR. Model
Performance Indicators (MPIs) such as root mean square error and correlation coefficient are used to judge the
performance of the probability distributions adopted for rainfall estimation. Based on GoF tests results and MPIs
values, P3 distribution is identified as the best suited amongst six distributions studied for modelling AMR for rainfall
estimation for the stations under study.


Chi-square, Kolmogorov-Smirnov, Mean Square Error, Correlation, Rainfall

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