| The application of the Log-normal distribution in the reliability field is very extensive. The fitting results between the lognormal distribution and Life data and Population income data are very well. Parameter estimation method, as the core of the field of the Log-normal distribution, has been discussed a lot by the domestic and foreign intellectuals. A few of estimation methods have been put forward:the maximum likelihood estimation method、uniformly minimum variance unbiased estimation method and the Bayes estimation method are commonly used. In the case of large samples, all these methods can obtain accurate and stable results. In the case of small samples, we usually use Bayes estimation method. The structure of Log-normal distribution is commonly very complex, so, in the application of Bayesian estimation method to calculate the parameter estimation values, we usually encounter the case of integral cannot being calculated. The using of Gibbs method for the posterior density function requires too much, it’s unable to handle all situations. So this paper proposes a new method--Linear Bayes estimation method. It adopts the prior information, in the same time it avoids the tedious calculation of the posterior expectation. Basing on the accuracy and stability of the estimation results, we provide a display Bayes estimation solution of the parameters of Log-normal distribution. This paper gives the expression of Linear Bayes estimation by calculating first. Then, under the mean square error matrix criterion, we prove that Linear Bayes estimation method is more stable than the maximum likelihood estimation method and the uniformly minimum variance unbiased estimation method. Finally, by numerical calculation and comparing, we find that the approximate error between the Linear Bayes estimation results and Bayes estimation results decreases with the increasing of sample size. The final image of relative error function p=f(n) stably stays between the function n-3/2and n-2/3. |
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