Parameters Estimation and Application for the Asymmetric 3-Parameter Generalized Error Distribution

To fit the data with leptokurtosis and fat tail, a new asymmetric generalized error distribution model is proposed by introducing a skewness parameter to the generalized error distribution, and using two tail parameters to control the left tail and right tail, respectively. This model can flexibly fit asymmetric and fat-tailed data sets. Firstly, the basic properties of the model are discussed in detail, including the cumulative distribution function, the quantile function, the origin moment of each order and so on, and the sampling method of the random variable is given. Secondly, the procedure to estimate the parameters of the model with moment estimation, maximum likelihood method and Bayesian method are discussed respectively, and these three methods are compared by the simulated data generated by Markov Monte Carlo method. Finally, two applications to real data sets are reported to illustrate the performance of this new asymmetric generalized error distribution in fitting the data with leptokurtosis and asymmetry.