Gamma mixture of generalized error distribution

A new symmetric heavy-tailed distribution, namely gamma mixture of generalized error distribution is defined by scaling generalized error distribution with gamma distribution, its probability density function, k-moment, skewness and kurtosis are derived. After tedious calculation, we also give the Fisher information matrix, moment estimators and maximum likelihood estimators for the parameters of gamma mixture of generalized error distribution. In order to evaluate the effectiveness of the point estimators and the stability of Fisher information matrix, extensive simulation experiments are carried out in three groups of parameters. Additionally, the new distribution is applied to Apple Inc. stock (AAPL) data and compared with normal distribution, F-S skewed standardized t distribution and generalized error distribution. It is found that the new distribution has better fitting effect on the data under the Akaike information criterion (AIC). To a certain extent, our results enrich the probability distribution theory and develop the scale mixture distribution, which will provide help and reference for financial data analysis.