Comparing Methods of Estimation for Two-Parameter Gamma Distribution Using Rainfall Patterns in Nigeria (Published)
In other to improve the ability of decision-makers to prepare for and deal with the unforeseen circumstances resulting from climate change as consequences of precipitation fluctuations, extreme and torrential rainfall. It is important to provide a more complete understanding of the range and likelihood of rainfall patterns a location could receive using a probabilistic model whose parameters might complement or even replace such common measures as the mean, median, variance, minimum, maximum and quartile values as major descriptors of rainfall at such location. Daily precipitation totals can be approximated by the gamma distribution as it is bounded on the left at zero and positively skewed indicating an extended tail to the right which suit the distribution of daily rainfall and accommodate the lower limit of zero which constrains rainfall values. This paper presents the comparison between Maximum Likelihood Estimation (MLE) of closed & open form solutions and Method of Moment Estimation (MME) of location and scaling parameters of the two-parameter gamma distribution, the parameters were estimated using MME and MLE with their performance adjudged and the result obtained showed that the closed-form solution of the MLE outperformed the open form solution and MME by comparing their estimates for the scaling parameter.
Keywords: Closed-Form Solution Open Form Solution, Generalized Gamma Distribution, Positively Skewed, Rainfall Patterns, maximum likelihood, method of moments