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
Application of Newton Raphson Method to Non – Linear Models (Published)
Maximum likelihood estimation is a popular parameter estimation procedure however parameters may not be estimable in closed form. In this work, the maximum likelihood estimates from different distributions were obtained after the failure of the likelihood approach. The targeted models are Non Linear models with an application to a Logistic regression model. Although, obtaining the estimate of parameters for non linear models cannot be easily obtained directly. That is the solution is intractable. So there is a need to look else where, so as to obtain the solutions . In this work, R statistical package was used in performing the analysis. The result shows that convergence was attained at the 18th iteration out of 21. This also provides the values and the maximum estimate for β0 and β1.
Keywords: Intractable Functions, Likelihood Function, maximum likelihood
A TWO-GROUP CLASSIFICATION MODELS FOR BINARY VARIABLES (Published)
This paper is a study of two-group classification models for binary variables. Eight classification procedures for binary variables are discussed and evaluated at each of 118 configurations of the sampling experiments. The results obtained ranked the procedures as follows: Optimal, Linear discriminant, Maximum likelihood, Predictive, Dillon Goldstein, Full multinomial, Likelihood and Nearest neighbour. Also the result of the study show that increase in the number of variables improve the accuracy of the models.
Keywords: Binary Variables, Classification Models, Dillon Goldstein, Linear Discriminant, Misclassification, Optimal, Predictive, and Multinomial, maximum likelihood
A COMPARISON OF MULTIVARIATE DISCRIMINATION OF BINARY DATA (Published)
The use of classification rules for binary variables are discussed and evaluated. R-software procedures for discriminant analysis are introduced and analyzed for their use with discrete data. Methods based on the full multinomial, optimal, maximum likelihood rule and nearest neighbour procedures are treated. The results obtained ranked the procedures as follows: optimal, maximum likelihood, full multinomial and nearest neighbour rule.
Keywords: Binary Data, Classification Rules, Full Multinomial, Nearest Neighbour, Optimal, maximum likelihood