A Study Of The Effect Of Fitting Real Data To The Skew-Normal Distribution

In this study,119 groups of multi-dimensional real data from multiple fields were collected.The maximum likelihood estimation and the improved EM algorithm are used to estimate the unknown parameters of the multi-dimensional normal and skew-normal distribution.On this basis,the fitting of multi-dimensional normal distribution and multi-dimensional skew-normal distribution to real data is compared from data expectation,covariance,and Mardia’s measurements of skewness and kurtosis the AIC,and BIC values of distribution fitting.The results show that: firstly,although the estimated values of expectation and covariance under the two distributions are different,their relative errors fluctuate within a certain range;secondly,the Mardia’s measurements of skewness and kurtosis values are higher under the assumption of the skew-normal distribution;Finally,the skew-normal distribution will produce smaller AIC and BIC values,so it can be considered that the skew-normal distribution is more suitable for fitting multidimensional real data.In addition,this study also investigates the fitting of skewed data from the perspective of data transformation.In this study,the multivariate skew-normal and multivariate normal distributions were fitted with the robust-transformed data to investigate the effect of the robust transformation on the fit of the data.The results show that the robust transformation can effectively reduce the skewness and kurtosis of the data without changing the data structure,making the data closer to a normal distribution.At last,this paper proposes a new distribution that fits the one-dimensional skewed data,i.e.,the G-N distribution,which provides a new option for biased data fitting.The distribution is based on the univariate normal distribution,and the skewness is adjusted by introducing a shape parameter: when0 < < 1,the data are right-skewed;when < 0,the data are left-skewed;and when = 0,the data are symmetric.In addition,some statistical properties of this distribution,including the expectation,variance,and skewness coefficients,are investigated,and on this basis,the QuasiNewton method is used to iterate and calculate the maximum likelihood estimates of the unknown parameters.Finally,a simple numerical application of the distribution using real data is carried out in this study.The combined results show that the one-dimensional G-N distribution proposed in this study,like the skew-normal distribution,can provide both a new option for fitting one-dimensional skewed data and a basis for a certain family of distributions to extend a new distribution with adjustable skewness.