Numerical characteristics and parameter estimation of finite mixed generalized normal distribution. Issue 7 (3rd July 2022)

• Record Type: Journal Article
• Authors: Wen, Luliang; Qiu, Yanjun; Wang, Minghui; Yin, Juliang; Chen, Pingyan
• Is Part Of: Communications in statistics. Volume 51:Issue 7(2022)
• Page Start: 3596
• Page End: 3620
• Publication Date: 2022-07-03
• Subjects: ECM algorithm -- Maximum likelihood estimation -- Mixed generalized normal distribution -- Numerical characteristics; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2020.1720733
• Languages: English
• ISSNs: 0361-0918

Abstract

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.