Abstract
The paper extends earlier work on the so-called skew-normal distribution, a family of distributions including the normal, but with an extra parameter to regulate skewness. The present work introduces a multivariate parametric family such that the marginal densities are scalar skew-normal, and studies its properties, with special emphasis on the bivariate case.
Keywords
Skew normal distributionSkewnessMathematicsSkewMultivariate statisticsMultivariate normal distributionBivariate analysisParametric statisticsScalar (mathematics)StatisticsKurtosisEconometricsDistribution (mathematics)Marginal distributionMathematical analysisComputer scienceGeometryRandom variable
Affiliated Institutions
Related Publications
Distributions Generated by Perturbation of Symmetry with Emphasis on a Multivariate Skew<i>t</i>-Distribution
Summary A fairly general procedure is studied to perturb a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric den...
On the Unification of Families of Skew‐normal Distributions
Abstract. The distribution theory literature connected to the multivariate skew‐normal distribution has grown rapidly in recent years, and a number of extensions and alternative...
Smooth centile curves for skew and kurtotic data modelled using the Box–Cox power exponential distribution
Abstract The Box–Cox power exponential (BCPE) distribution, developed in this paper, provides a model for a dependent variable Y exhibiting both skewness and kurtosis (leptokurt...
Semiparametric ARCH Models
This article introduces a semiparametric autoregressive conditional heteroscedasticity (ARCH) model that has conditional first and second moments given by autoregressive moving ...
Introduction to Multivariate Analysis
Part One. Multivariate distributions. Preliminary data analysis. Part Two: Finding new underlying variables. Principal component analysis. Factor analysis. Part Three: Procedure...
Publication Info
- Year
- 1996
- Type
- article
- Volume
- 83
- Issue
- 4
- Pages
- 715-726
- Citations
- 1644
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
1644
OpenAlex
Cite This
Adelchi Azzalini
(1996).
The multivariate skew-normal distribution.
Biometrika
, 83
(4)
, 715-726.
https://doi.org/10.1093/biomet/83.4.715
Identifiers
- DOI
- 10.1093/biomet/83.4.715