On Properties of the (Φ, a)-Power Divergence Family with Applications in Goodness of Fit Tests

Vonta, F; Mattheou, K; Karagrigoriou, A

dc.contributor.author	Vonta, F	en
dc.contributor.author	Mattheou, K	en
dc.contributor.author	Karagrigoriou, A	en
dc.date.accessioned	2014-03-01T02:11:49Z
dc.date.available	2014-03-01T02:11:49Z
dc.date.issued	2012	en
dc.identifier.issn	13875841	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29947
dc.subject	Divergence measures	en
dc.subject	Goodness of fit test	en
dc.subject	Limiting property	en
dc.subject	Multinomial populations	en
dc.subject	Order preserving property	en
dc.subject	Quadratic convergence	en
dc.title	On Properties of the (Φ, a)-Power Divergence Family with Applications in Goodness of Fit Tests	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s11009-010-9205-8	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s11009-010-9205-8	en
heal.publicationDate	2012	en
heal.abstract	In this paper we unify the different measures of divergence by introducing a general class of measures of divergence, the (Φ, a) -power divergence family and investigate its main properties including the limiting property, the order preserving property, and the quadratic convergence. For the practical implications of the proposed class of measures, we examine its use in goodness of fit tests for multinomial populations. In particular, a test statistic for goodness of fit tests based on the proposed family of measures is investigated for small sample sizes and various multinomial distributions that include symmetric, skewed and equiprobable models. The proposed statistic appears to work well in all cases considered as opposed to other traditional tests including the traditional chi-squared Pearson's test, which may work well in some but not all situations. © 2010 Springer Science+Business Media, LLC.	en
heal.journalName	Methodology and Computing in Applied Probability	en
dc.identifier.doi	10.1007/s11009-010-9205-8	en
dc.identifier.volume	14	en
dc.identifier.issue	2	en
dc.identifier.spage	335	en
dc.identifier.epage	356	en