Modelling Nigeria Rainfall Data Using Exponential Family of Distribution: A Comparative Study

In response to the growing concern about climate change, the study focuses on rainfall, a complex and challenging meteorological  variable to predict compared to temperature. This research introduces an innovative approach to model rainfall data, leveraging  probability distributions from the exponential family. The study utilizes secondary data encompassing monthly rainfall measurements in  millimeters (mm) spanning from 1986 to 2020, obtained from the Nigeria Meteorological Agency (NiMET) – covering a span of thirty-five  years. To identify the most suitable distribution, various model efficiency criteria, including log-likelihood, Kolmogorov-Smirnov test,  Cramer-Von Mises, Anderson Darling, and Akaike Information Criterion (AIC), are employed. The analysis highlights the Weibull  distribution as the most fitting model, exhibiting the highest likelihood value, along with the lowest values for the Kolmogorov-Smirnov  test, Cramer-Von Mises, Anderson Darling, and AIC. For six States under consideration: Abuja, Lagos, Edo, Kebbi, Taraba, and Enugu, the  study establishes the Weibull distribution as the superior choice. Notable log-likelihood and AIC values for each location reinforce its suitability for modeling rainfall data in Nigeria. Specifically, the log-likelihood and AIC values for Abuja are 1910.155 and 3824.309,  respectively, and similar trends are observed across the other locations. Consequently, the study strongly recommends the adoption of  the Weibull distribution as the preferred model for rainfall data modeling in Nigeria. Additionally, it encourages further research into rainfall data modeling employing the Weibull distribution within the context of time series models, both with and without seasonality,  utilizing the well-established Box-Jenkins methodology