{"title":"Theoretical considerations when simulating data from the g-and-h family of distributions","authors":"Oscar Lorenzo Olvera Astivia, Kroc Edward","doi":"10.1111/bmsp.12274","DOIUrl":null,"url":null,"abstract":"<p>The <i>g</i>-and-<i>h</i> 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 <i>g</i>-and-<i>h</i> distribution may result in marginal distributions which are no longer <i>g</i>-and-<i>h</i> distributed, that more than one set of (<i>g,h</i>) parameters can correspond to the same values of population skewness and excess kurtosis, and that multivariate generalizations of <i>g</i>-and-<i>h</i> 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 (<i>g,h</i>) parameters are used to simulate data, even if they imply the same population values of skewness and excess kurtosis.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"British Journal of Mathematical & Statistical Psychology","FirstCategoryId":"102","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/bmsp.12274","RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
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.
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.