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 statisticalliterature. However, a combined approach of multiple tests remains underutilized, despite evidence supporting their improvedprecision. Increased erratic climatic conditions pose severe threats to economic stability, necessitating robust statisticalmethods for climate modeling. To address this need, this study evaluates probability distributions for climatic variables using acomprehensive 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 distributionexamined the influence of partitioning data into different segments (block sizes). The results show a generalized extremevalue (GEV) distribution consistently outperforming other distributions for temperature and rainfall data, across multiple metrics. Longer block sizes capture long-term climatic patterns but introduce greater uncertainty due to fewer data points, while shorterblock sizes tend to overfit. Intermediate block sizes provide a balance, producing reliable parameter estimates and stable returnlevels. These findings underscore the importance of selecting suitable block sizes and confirm the robustness of the GEVdistribution for climate modeling. The study contributes to improved methodologies for risk assessment and climate adaptationstrategies, particularly in regions such as Kenya.