A systematic approach to modeling monthly maximum temperature and total rainfall in Kenya

Goodness of fit (GOF) test approaches for selecting probability distributions of climatic variables are pervasive in the statistical literature. However, a combined approach of multiple tests remains underutilized despite evidence supporting their improved precision. Increased erratic climatic conditions pose severe threats to economic stability, necessitating robust statistical methods for climate modeling. To address this need, this study evaluates probability distributions for climatic variables using a comprehensive approach that combines multiple tests. A scoring system ranked each distribution's performance across tests, with a composite score indicating the best fit. To assess robustness, sensitivity analysis on the best-performing distribution examined the influence of partitioning data into different segments (block sizes). The results show a generalized extreme value (GEV) distribution consistently outperforming other temperature and rainfall data distributions across multiple metrics. Extended block sizes capture long-term climatic patterns but introduce greater uncertainty due to fewer data points, while shorter block sizes tend to overfit. Intermediate block sizes provide a balance, producing reliable parameter estimates and stable return levels. These findings underscore the importance of selecting suitable block sizes and confirm the robustness of the GEV distribution for climate modeling. The study contributes to improved methodologies for risk assessment and climate adaptation strategies, particularly in regions such as Kenya.