Numerical characteristics and parameter estimation of finite mixed generalized normal distribution
Luliang Wen, Yanjun Qiu, Ming-hui Wang, Juliang Yin, Pingyan Chen
Abstract
In this paper, a univariate finite mixed generalized normal distribution (MixGND) is proposed. First, we derive some probabilistic properties including hazard rate function, characteristic function, kurtosis and skewness, for a mixture of two generalized normal distributions. In particular, we use a geometric analysis and numerical simulation technique to study the monotonicity of skewness and kurtosis from prescribing corresponding parameters. Then moment estimation and maximum likelihood estimation of parameters are also given. To use the maximum likelihood estimation (MLE) method, an expectation conditional maximization (ECM) algorithm is proposed to estimate and numerically simulate seven parameters of a two-component MixGND under the same variance and heteroscedasticity. By using data sets of the S&P 500 and Shanghai Stock Exchange Composite Index (SSEC), we compare goodness-of-fit performance between the mixture of two generalized normal distributions and the mixture of two normal distributions. The empirical analysis results show that the former better describes the heavy-tailed and leptokurtic characteristics of the daily returns.