Theoretical considerations when simulating data from the g-and-h family of distributions

IF 1.5 3区 心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS British Journal of Mathematical & Statistical Psychology Pub Date : 2022-05-30 DOI:10.1111/bmsp.12274
Oscar Lorenzo Olvera Astivia, Kroc Edward
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Abstract

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.

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模拟g和h族分布数据时的理论考虑
g和h族分布是一种计算效率高、灵活的非正态数据建模和模拟方法。尽管这些发行版很受欢迎,但在使用它们时,有几个理论方面需要特别考虑。本文就这些方面进行了探讨。特别地,通过数学分析表明,流行的g- h分布的多元推广可能导致不再是g- h分布的边际分布,多组(g,h)参数可以对应相同的总体偏度和过量峰度值,文献中可用的g- h分布的多元推广是高斯copula分布的特殊情况。一个小规模的模拟也被用来证明当使用不同的(g,h)参数来模拟数据时,即使它们意味着相同的偏度和过量峰度的总体值,模拟结论是如何变化的。
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来源期刊
CiteScore
5.00
自引率
3.80%
发文量
34
审稿时长
>12 weeks
期刊介绍: The British Journal of Mathematical and Statistical Psychology publishes articles relating to areas of psychology which have a greater mathematical or statistical aspect of their argument than is usually acceptable to other journals including: • mathematical psychology • statistics • psychometrics • decision making • psychophysics • classification • relevant areas of mathematics, computing and computer software These include articles that address substantitive psychological issues or that develop and extend techniques useful to psychologists. New models for psychological processes, new approaches to existing data, critiques of existing models and improved algorithms for estimating the parameters of a model are examples of articles which may be favoured.
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