Construction And Comparative Study Of A New Combination Distribution Model

Theory of combinatorial distribution has been promoted and developed by relevant scholars and applied to various fields,since it was put forward in 2005.However,the weight and the threshold point of the combined distribution make it difficult to construct it sharply.It is difficult to solve the weight,and the requirement of the threshold point’s continuity and derivation may not be met by any two distributions.So,the two distributions selected according to the actual data distribution form may not be successful in constructing the combined distribution.Therefore,this paper attempts to construct a combined distribution model of on weight and threshold point to reduce the difficulty of constructing the combined distribution.Firstly,based on the folded method,this paper chooses a single distribution instead of two distributions to construct a folded combination distribution model.The extremum point of unimodal distribution density function has the property of zero derivative.The paper takes its extremum point as the boundary,discards the part that aren’t folded,keeps the rest and folds it with the axis of x=0 as the symmetry axis.Then the help of translation,compression and other changes makes the reserved part and the folded part form a complete distribution together,thus completing the construction of folding combined distribution.Based on folded method,the combined distribution model need not be constructed by connecting two distributions and solving weight,which increase the possibility of successful construction of combined distribution.Secondly,based on the research needs of the peak-tailed data in reality,this paper chooses the Gamma distribution as a single distribution,and constructs four kinds of folded Gamma combination distribution.The right-tailed thick-tailed feature of Gamma distribution is very suitable for describing the thick-tailed data;At the same time,the kurtosis coefficient of Gamma distribution is controlled by shape parameters,which also has advantages in describing the peak characteristics of data.Therefore,this paper takes Gamma distribution as an example to construct four kinds of folded Gamma combination distribution,which provides another choice for describing the distribution form of peak and thick tail data.Finally,numerical simulation shows that moment estimation and maximum likelihood estimation have good effects on parameter estimation of four kinds of folded Gamma combination distribution.Compared with normal distribution,the comparative study of real data proves that the four distributions have advantages in fitting the peak and thick tail data.In numerical simulation,200 sets of moment estimation and maximum likelihood estimation are carried out under increasing samples,respectively.The results show that the two estimation methods are effective in estimating four kinds of folded Gamma combination distributions.On the other hand,using the Shanghai and CSI 300 Index Returns and the monthly CPI data of the United States,this paper makes an empirical comparative study on the folded Gamma combination distribution.The results show that the fitting effect of the folded Gamma combination distribution is obviously better than that of the normal distribution,that is,the folded gamma combination distribution can effectively fit the peak and thick tail data.