How to select the right parametric model for daily precipitation ? Impact of distribution tails on goodness-of-fit test

Modeling the distribution of precipitation data is required in many applications regarding water resource management and planning, such as flood and drought events. A critical step in statistical modeling is to find probability distributions that correctly describe the occurrences and intensities of precipitation. The statistical modeling of daily precipitation via parametric distribution is often done using the Gamma, Pearson Type 3, and Weibull distributions. However, these statistical models used for precipitation have many drawbacks. As these models are either light or heavy-tailed, they are not suited for applications in large areas with varying tail characteristics. Over the last few years, multiple models of probability distributions of precipitation in compliance with extreme value theory on both ends of the spectrum have been developed, such as the Extended Generalized Pareto Distributions (EGPD). In particular, the EGPD family allows for an adaptable distribution that can model both low and extreme precipitations while dealing with the flexibility of modeling light and heavy tails. When it comes to testing the goodness-of-fit of parametric distributions, the Kolmogorov-Smirnov test is often referred to. However, this test fails to detect divergence in the tails of distributions, making it unfit for discriminating between distributions that must be well fitted to extreme precipitation events. A fast and efficient test called the exact Berk-Jones statistical test (also referred to as the Calibrated Kolmogorov-Smirnov test) is investigated. This test allows for theoretically better power for diverging extreme tails. In this study, the exact Berk-Jones statistical test is compared to the classical Kolmogorov-Smirnov test on multiple parametric distributions, including the EGPD, on a 38-year high-resolution grid dataset of daily precipitation over France.