Skew-Symmetric-Laplace Distributions And Their Applications

The skew-symmetric-Laplace distributions is a kind of skewed distribution,which is characterized by adding a skewness coefficient to make the model more flexible.Skew Laplace distribution has not only theoretical research value,but also practical application,such as flow cytometry data in microorganisms,and has achieved good results in image and numerical aspects.Parameter estimation is an important part of statistics and one of the main contents of this paper.The commonly used parameter estimation methods are Moment Estimation and Maximum Likelihood Estimate.The basic idea of Moment Estimation is to replace the corresponding total moment with sample moment.The basic idea of MLE:if an event occurs,the parameter estimation should be the most favorable one.In this paper,the parameter estimation of the two models is studied.The main content of this article is introduced belowIn this paper,we first define the skew-symmetric-Laplace distribution and obtain some simple properties.Then,we discuss several kinds of skew-symmetric distribution generated by the distribution function of Laplace distribution,including skew normal Laplace distribution,skew Laplace distribution,skew logistic Laplace distribution,skew triangular Laplace distribution,and give the probability density function diagrams of these distributions under different skewnessThen,this paper introduces the definition of linear regression model under the skew normal Laplace data,discusses the maximum likelihood estimation of model parameters,describes the Nelder Mead algorithm and how to generate the random number of model response variables.Under the AIS data set,it is shown that for the data with asymmetric characteristics,the use of the skew normal Laplace distribution is better than the use of the normal distribution.There are many ways to study the skew Laplace distribution,one of which is to discretize the continuous skew Laplace distribution to get a new discrete distribution,and then study the new discrete distribution.There are many definitions of skew Laplace distribution.In this paper,two definitions are involved.The first is proposed by Kotz et al.And the second is first proposed by Gupta et al.Based on the first form,kozubowski and barbiero use two different discretization methods to get two different discrete distributions.In the last part of this paper,according to this idea,based on the second definition,we get a new discrete distribution:two parameter discrete skew Laplace distribution.Then we study some properties and digital characteristics of the distribution,and introduce three methods of parameter estimation.Through Monte Carlo simulation,we show the good estimation results of the three methods,and compare the three methods.Then under the DMFT data set,AIC value is used as the standard of evaluation model.By comparing with two kinds of discrete models proposed by kozubowski and barbiero,it shows that the new model is also an alternative model for fitting data.