Estimation Of Parameters Of The Gamma Distribution Under Different Loss Functions

Parameter estimation are common research problems in Bayesian statistics inference and statistics decision.This paper is modeled on distribution under Jeffreys priori and include Bayesian estimation,minimax estimation,admissibility,posterior expected loss and other parameter estimations based on distribution under different loss function.This paper mainly discusses the relationships of Bayesian estimation,minimax estimation,admissibility,posterior expected loss under different loss functions.We proved the Bayesian estimations based on distribution under Jeffreys priori of weighted square error loss and balanced weighted square error loss are admissibility minimax estimation and the corresponding posterior expected loss is the same as minimax risk value.We also proved that the admissibility minimax estimation of entropy loss function and the Bayesian estimation of balance entropy loss function is admissible.Moreover,the Bayesian estimation of Q-symmetric entropy loss function is admissible minimax estimation and the Bayesian estimation admissibility of Q-symmetric entropy loss function,posterior expected loss of Q-symmetric entropy loss function being the same as its minimax risk value are all proved.This paper is organized into six chapters : The first chapter is the introduction.We introduce the current research status of balance loss function,minimax estimation,and admissibility and list what we have contributed.The second chapter is the preliminary.We mainly cover the conjugate prior, non-informative prior,loss function,Bayesian estimation,minimax estimation,admissibility,maximum likelihood estimates,and posterior expectations loss values.The third chapter is about the parameter estimation of weighted square error loss and balanced weighted square error loss.The fourth chapter is about parameter estimation of entropy loss function and balance entropy loss function.The fifth chapter is about parameter estimation of Q-symmetric entropy loss function and balanced Q-symmetric entropy loss function.The sixth chapter is numerical simulation.The seventh chapter is the conclusion and prospect,summarizing the main work of this paper and prospects.