Generalized skew-elliptical distributions and their quadratic forms

被引：0
作者：
Marc G. Genton
Nicola M. R. Loperfido
机构：
[1] Texas A&M University,Department of Statistics
[2] Università degli Studi di Urbino,Instituto di scienze Economiche, Facoltá di Economia
来源：
Annals of the Institute of Statistical Mathematics | 2005年 / 57卷
关键词：
Elliptical distribution; invariance; kurtosis; selection model; skewness; weighted distribution;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper introduces generalized skew-elliptical distributions (GSE), which include the multivariate skew-normal, skew-t, skew-Cauchy, and skew-elliptical distributions as special cases. GSE are weighted elliptical distributions but the distribution of any even function in GSE random vectors does not depend on the weight function. In particular, this holds for quadratic forms in GSE random vectors. This property is beneficial for inference from non-random samples. We illustrate the latter point on a data set of Australian athletes.
引用
收藏
页码：389 / 401
页数：12
相关论文
共 32 条
[1]  
Arnold B. C.(2000)The skew-Cauchy distribution Statistics and Probability Letters 49 285-290
[2]  
Beaver R. J.(1985)A class of distributions which includes the normal ones Scandinavian Journal of Statistics 12 171-178
[3]  
Azzalini A.(1999)Statistical applications of the multivariate skew normal distribution Journal of the Royal Statistical Society Series B 61 579-602
[4]  
Azzalini A.(1996)The multivariate skew-normal distribution Biometrika 83 715-726
[5]  
Capitanio A.(1983)Conditional independence in statistics Sankhya A 45 324-337
[6]  
Azzalini A.(2001)A general class of multivariate skew-elliptical distributions Journal of Multivariate Analysis 79 99-113
[7]  
Dalla Valle A.(1997)Inference from non-random samples (with discussion) Journal of the Royal Statistical Society Series B 59 55-95
[8]  
Basu D.(2001)Moments of skew-normal random vectors and their quadratic forms Statistics and Probability Letters 51 319-325
[9]  
Pereira C. A. B.(1968)Multivariate normal plotting Applied Statistics 17 157-161
[10]  
Branco M. D.(1982)Robustness in real life: A study of clinical laboratory data Biometrics 38 377-396
1234