Parameter Estimation Of The Skew Normal Distribution And Its Application In Environmental Data

The normal distribution is often used to fit real data,but in fact most of the data in many fields are not strictly symmetric,so using a more general skewed distribution to study and describe the data can more accurately characterize the nature of the analyzed data.Since Azzalini proposed the skew normal distribution,many scholars began to study the skewed distribution,in addition to discussing its definition and properties,parameter estimation has been a hot issue in the research of scholars at home and abroad.The classical parameter estimation method is also applied to the parameter estimation of skew normal distribution,and one of the major difficulties of the current parameter estimation is that all the parameter estimation methods under small samples are not good for the estimation of shape parameters.In view of this difficulty,this paper proposes a new parameter estimation method: on the basis of the maximum likelihood estimation method,a constraint is added,that is,the maximum likelihood estimation method with constraints.In this paper,the effectiveness and robustness of the parameter estimation method are first proved by simulation,and the method is applied to the regression model,which relaxes the assumption that the error term in the regression model follows the normal distribution,and proves the validity of the parameter estimation of the method with simulation data.In terms of application,two small sample datasets were selected: air quality data in Chengdu,Guiyang and Kunming and arsenic content data in Mekong Delta region for empirical analysis,and the parameter estimation results obtained by the method proposed in this paper were more suitable for the data in ordinary skew normal data.In the skew normal regression model,the effect of different parameter estimation methods in prediction is compared,and it is concluded that the parameter estimation effect can improve the prediction effect to a certain extent,and a new and simpler parameter estimation method is improved for the parameter estimation of the skew normal regression model.The innovations of this paper are as follows:(1)A new estimation method is proposed for the estimation of skew normal distribution parameters,which adds a constraint to the ordinary maximum likelihood estimation to solve the problem that the previous skew normal distribution parameter estimation method has a poor estimation effect in small samples,especially for shape parameter estimation,so that the estimation effect also performs well in small samples.(2)The assumption that the error terms of the multiple linear regression model obey the normal distribution are relaxed in the regression model,and the method in this paper is applied to the regression model to establish a skew normal multiple linear regression model,which provides a new parameter estimation method for the skew normal multiple linear regression model,and improves the effectiveness of parameter estimation of the skew normal multiple linear regression model,and compares the prediction effect of the three predictors of different parameter estimation methods.