Modeling of Daily Precipitation Amounts Using the Mixed Gamma Weibull Distribution

TL;DR

This paper introduces a unified framework using the Mixed Gamma Weibull distribution to select the best probability model for daily precipitation amounts, improving modeling accuracy.

Contribution

It develops a model selection framework based on the MGW distribution that encompasses common distributions like exponential, Gamma, and Weibull.

Findings

The MGW distribution effectively models daily precipitation data.

Likelihood ratio tests facilitate model selection within the MGW framework.

The framework improves the accuracy of precipitation modeling.

Abstract

By recognizing that the main difficulty of the modeling of daily precipitation amounts is the selection of an appropriate probability distribution, this study aims to establish a model selection framework to identify the appropriate probability distribution for the modeling of daily precipitation amounts from the commonly used probability distributions, i.e. the exponential, Gamma, Weibull, and mixed exponential distributions. The mixed Gamma Weibull (MGW) distribution serves this purpose because all the commonly used probability distributions are special cases of the MGW distribution, and the MGW distribution integrates all the commonly used probability distributions into one framework. Finally, via the large sample inference of likelihood ratios, a model selection criterion can be established to identify the appropriate model for the modeling of daily precipitation amounts from the MGW distribution framework.