Reasearch On Shape Estimation For The Two-parameter Gamma Distribution

Gamma distribution is a frequently-used statistical distribution. Since Gamma distribution was presented by Frery, it has attracted scholars’ great attention and been developed a lot. The foreground of the distribution is very wide. It has been widely used in navigation, budget, astronomy and medicine. From now on, many scholars have studied the parameter of Gamma distribution. However, there isn’t a proper method to estimate the parameter of Gamma distribution which makes this distribution little application.In this paper, we summarize several classical Gamma distribution parameter estimation method and prove the uniqueness, consistent and asymptotic behavior of shape parameter by the method of moment thought. Then through the characteristics of the sample variation coefficient, the estimation of the shape parameter and scale parameter of the Gamma distribution are obtained. Then we compare several estimation mentioned in this paper by the Monte Carlo simulation from the aspects of bias and efficiency. The results show that the proposed method has certain advantages.