Comparative Assessment of Two Estimates of the Bernoulli Distribution Parameters in the Analysis of Short-Term Rainfall Intensity

Abstract

This paper presents an application of the maximum likelihood method and the Bernoulli distribution of selected rainfall intensity data. The parameter of the density of Bernoulli distribution was estimated by the maximum likelihood method (MLM), and Microsoft Excel Solver (MES). The calculated 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 revealed that the Bernoulli probability distribution’s parameter (p) is the mean of the natural logarithm of rainfall intensity using the MLM estimator. The parameter were 0.665 and 0.535 for Makurdi, 0.695 and 0.478 for Abeokuta using MLM and MES, respectively. The relative errors were 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 0.876 and 0.800, and 0.269 and 0.341, 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. There is a need to evaluate MLM and other probability distributions