Estimation and Fitting Rainfall Pattern Distribution in Ghana using the Expectation-Maximization Algorithm with some Probability Models

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October 9, 2016
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The study investigated the rainfall pattern estimation involving fteen selected rainfall stations across Ghana for the period of sixteen years (2000-2015) with the main objective of estimating the missing values and determining the annual average rainfall values for the period under study. The observed data was tted with three probability distributions which were; Gamma, Lognormal and Normal. Goodness-of- t tests were conducted in order to select the best model t. These included Kolgmorov-Smirnov, Cramer-von Mises and Anderson-Darling tests to- gether with the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The normal probability distribution was selected as the best model since it provided the minimum goodness-of- t test statistic values. The EM algorithm which has the capability to deal with missing values was used to complete the missing data and together with the normal distribution, esti- mated the average rainfall values of the various stations. The estimates of the EM algorithm were observed to be better estimates for the data because they were smaller than the regular estimates and also provided the least log-likelihood values. Therefore, we recommend that the Expectation-Maximization algorithm (Normal EM algorithm) should be used to estimate the missing values as well as the annual average rainfall of the daily rainfall data recorded in Ghana.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology In partial fulfillment of the requirement for the Degree of M.Phil Mathematical Statistics.