A new alpha logarithmic-generated class to model precipitation data with theory and inference

Precipitation, or rainfall, is a central feature of the weather cycle and plays a vital role in sustaining life on Earth. However, existing models such as the Poisson, exponential, normal, log-normal, generalized Pareto, gamma, generalized extreme value, lognormal, beta, Gumbel, Weibull, and Pearson type III distributions used for predicting precipitation are often inadequate for precisely representing the complex pattern of rainfall. This study proposes a novel and innovative approach to address these limitations through the new alpha logarithmic-generated (NAL-G) class of distributions. The study authors thoroughly examine the NAL-G class and a unique model, the NAL-Exponential (NAL-Exp) distribution, with a focus on analyzing mathematical properties such as moments, quantile function, entropy, order statistics, and more. Six recognized classical estimation methods are employed, and extensive simulations are conducted to determine the best one. The NAL-Exp distribution demonstrates its high adaptability and value through its superior performance in modeling four distinct rainfall data sets. The results show that the NAL-Exp distribution outperforms other commonly used distribution models, highlighting its potential as a valuable tool in hydrological modeling and analysis. The increased versatility and flexibility of this new approach hold great potential for enhancing the accuracy and reliability of future rainfall predictions.