Abstract
This paper reports statistical goodness-of-fit evaluations of selected rainfall intensity duration data as a follow-up to previous studies on probabilities distribution. It is an application of Microsoft Excel Solver (MES) and the maximum likelihood method (MLM) to establish the performance of the Exponential distribution in predicting the distribution of selected rainfall intensity data. Rainfall intensity data from two locations in Nigeria (Makurdi and Abeokuta) was collected from the literature. The data was used to evaluate the potential of exponential probability distribution to predict and describe rainfall intensity. The constant in the probability distribution was determined using MLM and MES. The numerically determined constant of the density of Exponential distribution was estimated by the MLM and MES. The calculated Exponential probabilities using the estimated parameter 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 Exponential probability distribution’s parameter (λ) is the mean of the natural logarithm of rainfall intensity using the MLM estimator. The parameters were 1.665 and 0.783 for Makurdi, and 1.695 and 0.754 for Abeokuta using MLM and MES, respectively. The relative errors were 0.659 and 1.008, and 0.743 and 1.141 for Makurdi and Abeokuta using MLM and MES, respectively. The correlation coefficient for Makurdi and Abeokuta using MLM and MES were 0.826 and 0.800, and 0.470 and 0.344, respectively. It was concluded that the MLM parameter 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. It was concluded that the results are vital ingredients for the designers and managers of urban infrastructures. It was recommended that there is a need to evaluate the application of MLM and other probability distributions in environmental science and engineering

Key words: Exponential probability distribution, rainfall intensity, the goodness of fit test, maximum likelihood estimate method, Analysis of variance, Model of the Selection Criterion