Parameters Estimation And Application For The Skew Generalized Error Distribution

Researchers usually assume the random variable follows a normal distribution in the statistical data analysis process.In real life,however,it is more common that the skewness or kurtosis of data sets does not follow the normal distribution.Literature shows that the generalized error distribution is suitable to describe the data with leptokurtosis and fat tail,however,this distribution,including its special form of normal distribution and Laplace distribution,is a symmetric distribution,so it is not suitable to model the data with asymmetric distribution.In this paper,two skew generalized error distributions are proposed,the properties of which are discussed,and their usefulness in fitting data are studied.These skew generalized error distributions,which are proposed on the basis of the generalized error distribution,can fit the asymmetric,leptokurtosis and fat-tailed data better.The work in this paper goes in two steps:firstly,by introducing the skewness parameter in the way proposed by Azzalini(1985),a new skew 2-parameter generalized error distribution is proposed;furthermore,by introducing the skewness parameter and two tail parameters,modifying the skewness and tail of the generalized error distribution at the same time,a asymmetric generalized error distribution is proposed.Basic properties of these two distributions are studied.Different approaches to the estimation of parameters,such as moments,maximum likelihood and Bayesian method are discussed in detail,and these three methods are verified and compared with the simulation data generated by Markov Monte Carlo method.Finally,two applications to real data sets are reported respectively to illustrate the performance of these two new skew generalized error distributions in fitting the data with leptokurtosis and skewness.