Research On Methodes That Generalized ? Distribution Approximate Known Distribution

The generalized ? distribution is introduced in many subject areas such as independent principal component analysis of statistics,operations research,engineering studies.Mainly studies that how the generalized ? distribution fits the known probability density function.Firstly,based on the generalized ? distribution,and discuss its properties,the proving process of related theorem and the problem of effective area.The moment method and the percentile method are adopted to fit the known probability density function respectively.Finally,the definition of generalized ? distribution and the algorithm of fitting its known probability density function.The details are as follows:First of all,the theory of ? distribution has been rapidly developed in recent years,and various forms of promotion have been given one after another.In order to facilitate the discussion,some basic knowledge are given,such as the definition of generalized ? distribution,the parameter space of generalized ? distribution,the probability density function corresponding to generalized ? distribution.At the same time,the definition of generalized ? distribution and the problem of effective area are discussed.Secondly,based on the generalized ? distribution theory,the existence condition theorem of the origin moment of the generalized ? distribution is proved.In the same time,four existence conditions of mean,variance,skewness,kurtosis moment,and the Calculation formula of these four moments correspondingly are given.And its studied that how the calculation formula changes when the skewness parameters and kurtosis parameters interchange.Thirdly,using the moment method to fit the known probability density function and programming the algorithm in R language and giving the image of the fitting result.In order to compare with the known probability density function fitted by the moment method,the percentile probability method is used to fit the known probability density function.In the fitting algorithm,we program with matlab and give the images of the fitting results correspondly.Especially,when we use the percentile method to fit the known probability density function,the decimal point is accurate to the 16 th digit,which increases the accuracy of the fitting.Finally,the generalized ? distribution is extended based on previous studies.The definition meets required most of new function and the expression of the extending generalized ? distribution is given when k =3.At the same time,the algorithm flow of the function is given that the extending generalized ? distribution to fit the known probability density.