Derivation of the Fisher Information Matrix for 4-Parameter Generalized Gamma Distribution Using Mathematica

Abstract

AbstractFisher information matrix plays an important role in statistical inference of unknown parameters. Especially, it is used in objective Bayesian inference where we calculate the posterior distribution using a noninformative prior distribution, and also in an example of metric functions in geometry. To estimate parameters in a distribution, we can use the Fisher information matrix. Themore the number of parameters increases, the more its matrix form gets complicated. In this paper, by using Mathematica program swe derive the Fisher information matrix for 4-parameter generalized gamma distribution which is used in reliability theory. Key words : Fisher Information Matrix, Noninformative Prior Distribution, Reliability Theory, 4-Parameters Generalized Gamma Distribution 1. Introduction 1 4-parameter generalized gamma distribution is frequently used in reliability theory. To estimate four parameters, two methods can be considered. One is to use Jeffrey [1] prior distribution using the Fisher information matrix, and the other is to estimate the parameters from a posterior distribution by inducing non-informative prior distribution such as reference prior distribution etc. Thus, it is very important to obtain the Fisher information matrix. However, its form of the Fisher information matrix becomes complicated as the number of parameters increases. In order to solve this complexity, this paper uses Mathematica program to derive the Fisher information matrix for 4-parameter generalized gamma distribution. Generalized gamma distribution has been shown in Hargar and Bain