A Novel Alternative to the Beta and Kumaraswamy Distributions for Double Bounded Hydroclimatology Data

The beta distribution is considered the most popular for modeling double-bounded data, such as rates and percentages. But when it comes to double-bounded hydrological data, it often does not show an adequate fit to such data. As a better alternative to the beta, the Kumaraswamy distribution has appeared particularly promising for modeling hydrology and related areas. Nevertheless, both the beta and the Kumaraswamy distributions seldom succeed in providing an optimal fit in all cases. Thereby, in this study, a novel alternative is proposed, referred to as generalized unit Weibull distribution (GUWD), which has three parameters for modeling double-bounded hydrology data. Some statistical characteristics are introduced, such as the quantile function, Bowley skewness, Moors kurtosis coefficients, and moments. The maximum likelihood estimation (MLE) and the Bayesian estimation (BE) techniques are applied to estimate the GUWD’s parameters. To assess the performance of the MLE and BE, a Monte Carlo simulation study was performed. Finally, we show the superiority of our model using 38 empirical applications of the daily minimum relative humidity records in mainland China. The fit results and goodness-of-fit tests show that our proposed model outperforms the beta and Kumaraswamy distributions for modeling these datasets.