A Skew Extension of the<i>T</i>-Distribution, with Applications

Jones, M. C.; Faddy, M. J.

doi:10.1111/1467-9868.00378

Cited by 277 publications

(209 citation statements)

References 29 publications

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“…In other words, I am using the t distribution merely as a convenient way to describe data; I am not using the t distribution to conduct a t test. There is a large literature on the use of the t distribution to describe outliers (e.g., Damgaard, 2007;Jones & Faddy, 2003;Lange, Little, & Taylor, 1989;Meyer & Yu, 2000;Tsionas, 2002;Zhang, Lai, Lu, & Tong, in press). Methods of estimation that accommodate outliers are known as robust.…”

Section: A Descriptive Model For Two Groupsmentioning

confidence: 99%

Bayesian Estimation Supersedes the t Test

Kruschke¹

2012

PsycEXTRA Dataset

315

412

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Bayesian estimation for 2 groups provides complete distributions of credible values for the effect size, group means and their difference, standard deviations and their difference, and the normality of the data. The method handles outliers. The decision rule can accept the null value (unlike traditional t tests) when certainty in the estimate is high (unlike Bayesian model comparison using Bayes factors). The method also yields precise estimates of statistical power for various research goals. The software and programs are free and run on Macintosh, Windows, and Linux platforms.Keywords: Bayesian statistics, effect size, robust estimation, Bayes factor, confidence interval One of the most frequently encountered scientific procedures is a comparison of two groups (e.g., du Prel, Röhrig, Hommel, & Blettner, 2010;Fritz, Morris, & Richler, 2012;Wetzels et al., 2011). Given data from two groups, researchers ask various comparative questions: How much is one group different from another? Can we be reasonably sure that the difference is non-zero? How certain are we about the magnitude of difference? These questions are difficult to answer because data are contaminated by random variability despite researchers' efforts to minimize extraneous influences on the data. Because of "noise" in the data, researchers rely on statistical methods of probabilistic inference to interpret the data. When data are interpreted in terms of meaningful parameters in a mathematical description, such as the difference of mean parameters in two groups, it is Bayesian analysis that provides complete information about the credible parameter values. Bayesian analysis is also more intuitive than traditional methods of null hypothesis significance testing (e.g., Dienes, 2011).This article introduces an intuitive Bayesian approach to the analysis of data from two groups. The method yields complete distributional information about the means and standard deviations of the groups. In particular, the analysis reveals the relative credibility of every possible difference of means, every possible difference of standard deviations, and all possible effect sizes. From this explicit distribution of credible parameter values, inferences about null values can be made without ever referring to p values as in null hypothesis significance testing (NHST). Unlike NHST, the Bayesian method can accept the null value, not only reject it, when certainty in the estimate is high. The new method handles outliers by describing the data as heavy tailed distributions instead of normal distributions, to the extent implied by the data. The new method also implements power analysis in both retrospective and prospective forms.The analysis is implemented in the widely used and free programming languages R and JAGS and can be run on Macintosh, Linux, and Windows operating systems. Complete installation instructions are provided, along with working examples. The programs can also be flexibly extended to other types of data and analyses. Thus, the software can be used by virtually ...

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Section: A Descriptive Model For Two Groupsmentioning

confidence: 99%

Bayesian Estimation Supersedes the t Test

Kruschke¹

2012

PsycEXTRA Dataset

315

412

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“…Examples of such work are in Jones (2001Jones ( , 2002, Jones and Faddy (2003) and Bauwens and Laurent (2005). There is also a univariate skewed t distribution, which was introduced by McDonald and Xu (1995).…”

Section: Introductionmentioning

confidence: 99%

Asset pricing and portfolio selection based on the multivariate extended skew-Student-t distribution

Adcock

2009

Ann Oper Res

122

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The returns on most financial assets exhibit kurtosis and many also have probability distributions that possess skewness as well. In this paper a general multivariate model for the probability distribution of assets returns, which incorporates both kurtosis and skewness, is described. It is based on the multivariate extended skew-Student-t distribution. Salient features of the distribution are described and these are applied to the task of asset pricing. The paper shows that the market model is non-linear in general and that the sensitivity of asset returns to return on the market portfolio is not the same as the conventional beta, although this measure does arise in special cases. It is shown that the variance of asset returns is time varying and depends on the squared deviation of market portfolio return from its location parameter. The first order conditions for portfolio selection are described. Expected utility maximisers will select portfolios from an efficient surface, which is an analogue of the familiar meanvariance frontier, and which may be implemented using quadratic programming.

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“…The special case of the symmetric Student-t distribution is mentioned by Prause (1999) as a limit of the generalized hyperbolic with a reference to an unpublished report of Blaesild. Other references are BarndorffNielsen and Shephard (2001), Jones and Faddy (2003), Mencía and Sentana (2004), Demarta and McNeil (2005), Aas and Hobaek Haff (2005), and Aas and Hobaek Haff (2006). The most extensive discussion is in the last-mentioned paper.…”

Section: The Skew Hyperbolic T Distributionmentioning

confidence: 99%

Moments of the generalized hyperbolic distribution

et al. 2010

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In this paper we demonstrate a recursive method for obtaining the moments of the generalized hyperbolic distribution. The method is readily programmable for numerical evaluation of moments. For low order moments we also give an alternative derivation of the moments of the generalized hyperbolic distribution. The expressions given for these moments may be used to obtain moments for special cases such as the hyperbolic and normal inverse Gaussian distributions. Moments for limiting cases such as the skew hyperbolic t and variance gamma distributions can be found using the same approach.

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A Skew Extension of theT-Distribution, with Applications

Cited by 277 publications

References 29 publications

Bayesian Estimation Supersedes the t Test

Bayesian Estimation Supersedes the t Test

Asset pricing and portfolio selection based on the multivariate extended skew-Student-t distribution

Moments of the generalized hyperbolic distribution

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