On Mardia's and Song's measures of kurtosis in elliptical distributions
| dc.contributor.author | Zografos, K. | en |
| dc.date.accessioned | 2015-11-24T17:26:14Z | |
| dc.date.available | 2015-11-24T17:26:14Z | |
| dc.identifier.issn | 0047-259X | - |
| dc.identifier.uri | https://olympias.lib.uoi.gr/jspui/handle/123456789/13170 | |
| dc.identifier.uri | https://doi.org/10.1016/j.jmva.2007.05.001 | |
| dc.rights | Default Licence | - |
| dc.subject | elliptically contoured distributions | en |
| dc.subject | mardia's measure of kurtosis | en |
| dc.subject | song's measure of kurtosis | en |
| dc.subject | renyi entropy | en |
| dc.subject | shannon entropy | en |
| dc.subject | multivariate skewness | en |
| dc.subject | renyi | en |
| dc.title | On Mardia's and Song's measures of kurtosis in elliptical distributions | en |
| heal.abstract | The main objective of this paper is the calculation and the comparative study of two general measures of multivariate kurtosis, namely Mardia's measure beta(2,p) and Song's measure S(f). In this context, general formulas for the said measures are derived for the broad family of the elliptically contoured symmetric distributions and also for specific members of this family, like the multivariate t-distribution, the multivariate Pearson type II, the multivariate Pearson type VII, the multivariate symmetric Kotz type distribution and the uniform distribution in the unit sphere. Analytic expressions for computing Shannon and Renyi entropies are obtained under the elliptic family. The behaviour of Mardia's and Song's measures, their similarities and differences, possible interpretations and uses in practice are investigated by comparing them in specific members of the elliptic family of multivariate distributions. An empirical estimator of Song's measure is moreover proposed and its asymptotic distribution is investigated under the elliptic family of multivariate distributions. (c) 2007 Elsevier Inc. All fights reserved. | en |
| heal.access | campus | - |
| heal.fullTextAvailability | TRUE | - |
| heal.journalName | Journal of Multivariate Analysis | en |
| heal.journalType | peer reviewed | - |
| heal.language | en | - |
| heal.publicationDate | 2008 | - |
| heal.publisher | Elsevier | en |
| heal.recordProvider | Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μαθηματικών | el |
| heal.type | journalArticle | - |
| heal.type.el | Άρθρο Περιοδικού | el |
| heal.type.en | Journal article | en |
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