Early information for sustainable utilization of water resources through poisson probability distribution of rainfall is an important regulatory measure for flood control and water security management. As a follow-up to our previous studies on distributions, this paper reports statistical goodness-of-fit evaluations of selected rainfall data. It is the utilization of the maximum likelihood method (MLM) for the poisson probability distribution (PPD)of selected rainfall data. The numerically estimated constant of the density of PPD was estimated by the MLM, and Microsoft Excel Solver (MES). These estimated constants were used to compute probabilities of poisson distributions. The computed probabilities using the constants obtained were evaluated statistically (analysis of variance, (ANOVA), relative error, model of' selection criterion (MSC), Coefficient of Determination (CD) and Correlation coefficient (R). The study established that the poisson probability distribution’s parameter (p) was the average of the logarithm to base 10 of rainfall using the MLM and MES estimators. The constants were found to be 0.665 and 0.535 for Makurdi, 0.695 and 0.478 for Abeokuta using MLM and MES, respectively. The relative errors were found to be 0.479 and 0.743, and 1.141 and 1.509 for Makurdi and Abeokuta using MLM and MES, respectively. The correlation coefficient for Makurdi and Abeokuta using MLM and MES were found to be 0.876 and 0.800, and 0.269 and 0.341, respectively. It was concluded that the MLM constant was better than MES based on the values of MSC, CD, relative error and R. MLM predicted Weibull probability of rainfall intensity better than MES. Utilization of PPD in the estimation of rainfall intensity will help in the prediction of rainfall for agriculture in attaining sustainable goal 2 (zero hunger), regulatory measures for flood control and water security management. There is a need to evaluate MLM and other probability distributions to further assist in attaining sustainable development goals.
Key words: Poisson distribution, rainfall intensity, the goodness of fit test, maximum likelihood method, Microsoft Excel Solver
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