Gamma Distribution And Gamma Regression

The Gamma distribution is one of the commonly-used distributions for probabilistic models.Such models could be applied in areas as hydrology and meteorology,reliability and survival analysis etc.Therefore,the parameter estimation of Gamma distribution especially the Gamma distribution research has important significance.This dissertation introduces the existing nature and parameter estimation methods of the Gamma distribution,then put forward a new method of parameter estimation.Finally under the criterion of mean square error(MSE),use MATLAB to compare the pros and cons of the three estimation methods.A lot of study has been focused on the multiple linear regression model,but in many practical problems,the response variables and their expectations are not satisfied the assumptions,so the generalized linear model,the direct extension of multivariate linear regression model,such as the Gamma regression model has been widely used.This dissertation makes a intensive research about the Gamma Regression.Firstly it introduces the definition and parameter estimation of Gamma regression model,then introduces two different methods to obtain the estimated value,finally one real examples is given to analyze these results.If the data set has outliers or strong influence points,the wrong conclusion may be got or the wrong regression model that is not consistent with the actual model.So identifying the outliers or strong influence points of the data set is an important task in data analysis.Statistical diagnosis is an important part of data analysis,its main task is to detect the known observation data whether satisfied with the postulated model and the conditions given or not.The point which doesn't meet in the postulated model or the conditions was called outliers or strong influence point.This dissertation introduces the basic statistical diagnosis model namely case-deletion model(CDM).Firstly we presents the definition and regression coefficients'estimate of this model,and the first-order approximation formula of the estimator.Then we introduce several statistical diagnostic statistics,such as Cook distance,likelihood distance,etc.Finally we calculate and compare these diagnosis statistics to find out the outliers or strong influence points.