Parameter Estimation of the Inverted Kumaraswamy Distribution by Using L-Moments Method: an Application on Precipitation Data

Abstract

Modeling precipitation data plays a critical role in water resource and flood management. Statistical distributions are frequently used in describing hydrological variables. Different distributions and estimation methods have been presented in previous studies for modeling precipitation data. In this study, the inverted Kumaraswamy distribution is considered for its advantageous properties, and the L-moments and maximum likelihood methods are employed in estimating the parameters of the inverted Kumaraswamy distribution. In the application part, the annual maximum monthly precipitations recorded in the Rize, Türkiye are modeled with the inverted Kumaraswamy distribution. To the best of the author’s knowledge, the L-moment method is considered for the first time to estimate the parameters of the inverted Kumaraswamy distribution. In addition, the efficiencies of the estimation methods are compared with a Monte-Carlo simulation study. For evaluating the performances of the estimation methods, the goodness of fit criteria including root mean square error, Kolmogorov Smirnov test, and coefficient of determination (R^2) are used in the application part of the study. The results show that for the data considered, the L-moments method yields more accurate results than the maximum likelihood method in estimating the parameters when the sample size is small. Accordingly, the corresponding distribution with L-moments estimations provides a better fit to precipitation data obtained from the Rize station.