Generalizing the Conjugate Lindley's Utility Function to Estimate the Multi Parameter Distributions Parameters

Abstract

Bayesian method is one of many methods inrroduced for estimating the parameters of the probability distributions, In this method the parameters of the distributions considered as random variables and has a probability distribution unlike other estimation methods. When estimating by the Bayesian method, the estimation is either directly or by using loss functions or using utility functions. The issue, however gets complicated as the number of estimated parameters increases, which makes the estimation process numerical because it is difficult to obtain analytical formulas. In our research, the method of estimating the parameters of the distributions has been generalized using the Lindley conjugate utility function with k parameters and that the parameters estimated in this way make the Lindley conjugate utility function the greatest possiblelity by obtaining the appropriate approximate optimal decisions, as this estimation method was clarified by applying it to the distribution of generalized gamma with three parameters and the estimators were found analytically.