Abstract
The aim of this study was to employ Maximum Likelihood (MLE) jointly with a numerical Method (Newton Raphson method) to obtain parameter estimates from the two-parameter Gamma model. The profile likelihood of the two-parameter Gamma model was also put into consideration. The methods were demonstrated using simulation studies and real life data considering data sets generated by R statistical software for different sample sizes. Standard errors were computed and 5 % Wald-confidence interval was constructed for the estimates of the model. The result of the study shows that Maximum Likelihood Estimation (MLE) jointly with Newton Raphson method was more efficient for estimating parameters of the Gamma model in simulation study than real life data. The study recommends that parameter estimates from the two-parameter Gamma model should be obtained by employing Maximum Likelihood Estimation jointly with Newton Raphson Method.
Highlights
The two-parameter gamma probability distribution has found much application in technology and natural sciences, more especially in the areas of failure and survival analysis
The estimation of the parameters of the two-parameter gamma distribution is of great importance and it has been discussed widely
In some cases, the maximum likelihood (MLE) is ineffective in terms of statistical or computation properties, in particular for Gamma Probability distribution
Summary
The two-parameter gamma probability distribution has found much application in technology and natural sciences, more especially in the areas of failure and survival analysis. The maximum likelihood (MLE) is the most commonly used method of parameter estimation due its efficiency and good theoretical properties, and its ease application which gives explicit algebraic estimates of a probability distribution. Other methods which have been proposed in the literature as an alternative to the MLE method include; the secant, the bisection and the Newton-Raphson Methods In both the secant and the bisection methods, the process converges slowly. MLE was used jointly with the Newton Raphson method which has the ability to find solutions where no closed form exist, ease of application and faster rate of convergence for the estimation of the parameters of two-parameter Gamma model using simulation studies and real life data
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