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General Exponential Distribution: Bayes Estimation under Entropy Loss Function

Author: Cyrille-Clovis Moypemna-Sembona（XiLin）
Tutor: WangDeHui
School: Jilin University
Course: Probability Theory and Mathematical Statistics
Keywords: Bayesian estimation Maximum likelihood estimation Gamma distribution Entropy Loss Function Unbiased estimate Invariant estimate Prior density function Posterior density function
CLC: O211.67
Type: Master's thesis
Year: 2010
Downloads: 10
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Abstract


In 1825 , Benjamin Gompertz introduced Gompertz-Makeham law . Use the following distribution function to describe the growth of mortality , let's consider a special case fact , Gupta Kundu (1999) , consider this model in ρ = 1 the special circumstances of the time , through the use of two - parameter exponential distribution . generalized exponential distribution function (Generalized Exponential) : density function for which α , and λ is the shape parameter and scale parameter in this article , we present a variety of generalized exponential distribution parameter estimation method , for example , the entropy loss function , Bayesian estimation , maximum likelihood estimation the optimal constant estimation process , and by comparing the simulation results in table 3.1 and 3.2 . fact , λ and α independent non- negative , and the prior distribution for obedience follows the gamma distribution priori variable : in the second chapter of this paper , we mainly discuss the above-mentioned three estimation methods are as follows : § 2.1 part of our main consideration maximum likelihood estimation (MLE) method ; § section 2.2 , we discuss the optimal constant entropy loss estimation process ; § 2.3 gives the Bayesian estimation method under the entropy loss estimated by these different methods , we can some important results are obtained as follows: where φ (λ) = λ solutions ( see ( 2.1.1 )) and its linear approximation formula is (see ( 2.37 )) , and by the Monte Carlo method can be ( see ( 2.40 )) . due to these parameter estimation method is difficult to estimate with explicit solution to represent Therefore , the third chapter focuses on how to use a computer numerical simulation method for the fitting of the parameters . fact , we MCMC method generates a random sample of the generalized exponential distribution so as to approximate the Bayes estimation of the unknown parameters . simulation, we get the data in table 3.1 and table 3.2 table 3.1 table 3.2 contrast results we can see , Bayes method in the sense of minimum mean square error (MSE) , the parameters α and λ estimated to be significantly better than the corresponding by the maximum likelihood method (MLE) parameter estimation .

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Theory of probability ( probability theory, probability theory ) > Random process > Expectations and Forecast
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