Some Q-Q probability plots to test spherical and elliptical symmetry

Runze Li, Kai Tai Fang, Li Xing Zhu

Research output: Contribution to journalArticle

38 Citations (Scopus)

Abstract

This article proposes some probability plots are proposed to test spherical and elliptical symmetry in terms of some invariant statistics under orthogonal transformations. Some correlation coefficients as numerical measures of detecting deviation from spherical or elliptical symmetry are recommended, and the empirical percentiles of these correlation coefficients are calculated by simulation. The simulation results for data sets from 12 different populations show that the new plots are useful for testing spherical and elliptical symmetry. Some discussion is given also.

Original languageEnglish (US)
Pages (from-to)435-450
Number of pages16
JournalJournal of Computational and Graphical Statistics
Volume6
Issue number4
DOIs
StatePublished - Jan 1 1997

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Probability Plot
Statistics
Symmetry
Correlation coefficient
Testing
Orthogonal Transformation
Percentile
Simulation
Deviation
Invariant

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty

Cite this

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abstract = "This article proposes some probability plots are proposed to test spherical and elliptical symmetry in terms of some invariant statistics under orthogonal transformations. Some correlation coefficients as numerical measures of detecting deviation from spherical or elliptical symmetry are recommended, and the empirical percentiles of these correlation coefficients are calculated by simulation. The simulation results for data sets from 12 different populations show that the new plots are useful for testing spherical and elliptical symmetry. Some discussion is given also.",
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Some Q-Q probability plots to test spherical and elliptical symmetry. / Li, Runze; Fang, Kai Tai; Zhu, Li Xing.

In: Journal of Computational and Graphical Statistics, Vol. 6, No. 4, 01.01.1997, p. 435-450.

Research output: Contribution to journalArticle

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