The VDR Test Of Generalized Gaussian Distribution

This paper is the application of VDR theory. We use randomized estimator defined bypivotal quantity to estimate parameters. And the probability density of randomized estimatoris just the fiducial density. Numerical simulations are carried out at the end of each sectionto illustrate the results about the research in R software. By the simulations, we analyse theconfidence interval by VDR, and compare it with data of classical inference of parameters. Thefull text is divided into four chapters.In chapter1, we introduce the development and research situation about the VDR theory.The trout’s conception of VDRis called as Type I VDR, and Type II VDR is proposed by YangZhenHai. The results on Type I are derived by using Type II VDR which is proposed for VDRTest. The classical tests will be derived when apply VDR test to certain cases, for examplet-test, and some new test are also derived. The confidence region are constructed by VDR hasthe smallest Lebesgue measure.In chapter2, we research the two parameter exponential distribution. The accurate distri-bution of pivotal quantity, which construct the probability density of randomized estimator, isderived. The VDR confidence interval is also established.In chapter3,we investigate the VDR test of Laplace distribution which is totally differentfrom exponential distribution. It is proved that any functions of the order statistics of Laplace arenot independent and not identical distributions. Therefore the maximum likelihood parameterestimations are used to construct approximate pivotal quantity. Finally we calculate the VDRconfidence interval.In chapter4, we mainly investigate a new distribution family-generalized Gaussian dis-tribution. By using the asymptotic normal distributions of the estimators which are maximumlikelihood method, we calculate the VDR confidence interval of three parameters. From theMonte Carlo simulations, it is concluded that the maximum likelihood method is found to besignificantly superior for heavy-tailed distributions than moment method.