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Theoretical considerations when simulating data from the g-and-h family of distributions
British Journal of Mathematical and Statistical Psychology ( IF 2.6 ) Pub Date : 2022-05-30 , DOI: 10.1111/bmsp.12274
Oscar Lorenzo Olvera Astivia 1 , Kroc Edward 2
Affiliation  

The g-and-h family of distributions is a computationally efficient, flexible option to model and simulate non-normal data. In spite of its popularity, there are several theoretical aspects of these distributions that need special consideration when they are used. In this paper some of these aspects are explored. In particular, through mathematical analysis it is shown that a popular multivariate generalization of the g-and-h distribution may result in marginal distributions which are no longer g-and-h distributed, that more than one set of (g,h) parameters can correspond to the same values of population skewness and excess kurtosis, and that multivariate generalizations of g-and-h distributions available in the literature are special cases of Gaussian copula distributions. A small-scale simulation is also used to demonstrate how simulation conclusions can change when different (g,h) parameters are used to simulate data, even if they imply the same population values of skewness and excess kurtosis.

中文翻译:

模拟来自 g 和 h 分布族的数据时的理论考虑

g -and - h系列分布是一种计算效率高、灵活的选项,用于对非正态数据进行建模和模拟。尽管它很受欢迎,但这些分布的几个理论方面在使用时需要特别考虑。本文探讨了其中一些方面。特别是,通过数学分析表明,g 和 h 分布的流行多元泛化可能导致边缘分布不再是gh分布,即超过一组 ( g,h) 参数可以对应于相同的总体偏度和超峰度值,并且文献中可用的gh分布的多元泛化是高斯 copula 分布的特例。小规模模拟也用于演示当使用不同的 ( g,h ) 参数模拟数据时模拟结论如何变化,即使它们暗示相同的偏度和过度峰度的总体值。
更新日期:2022-05-30
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