Application of the Length–Biased Weibull–Rayleigh Distribution to Fit the Rainy Season Rainfall for the Upper Ping River in Northern Thailand

Abstract

Statistical distributions are important and useful to determine the appropriate distributions for rainfall data and predict the return levels of rainfall data. The objectives of this study are to apply the length–biased Weibull–Rayleigh (LBWR) distribution for fitting the rainy season rainfall data and to predict the return levels of the rainy season rainfall data. The LBWR distribution is compared with the Rayleigh, Weibull, and Weibull–Rayleigh distributions to determine the best - fit for the rainy season rainfall data from 1957 to 2020 of Samoeng (Chiang Mai) and Mae Tha (Lamphun)stations in Thailand. From the Kolmogorov–Smirnov test, Anderson–Darling test and Akaike information criteria, the results show that the LBWR distribution is the best–fit distribution of the rainy season rainfall data for both stations. Based on the prediction of the return levels of the rainy season rainfall data, it shows that the rainy season rainfall at Samoeng station had higher return level than the rainy season rainfall at Mae Tha station. This could conclude that Samoeng district having a higher risk of flood compared to Mae Tha district. Therefore, the results from this study could be useful to formulate guidelines and strategies for flood irrigation and water management in Samoeng district.