Skip to main content
SpringerLink
Log in

Multi-sample tests for axial data from Watson distributions

  • Original Paper
  • Published:
AStA Advances in Statistical Analysis Aims and scope Submit manuscript

Abstract

The Watson distribution is one of the most used distributions for modeling axial data. In some situations, it is important to investigate if several Watson populations differ significantly. In this paper, we develop likelihood ratio tests and the ANOVA for testing the hypothesis of the equality of the directional parameters of several Watson distributions with different concentrations. We also determine the empirical power of the ANOVA and LR tests for some dimensions of the sphere.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anderson, C.M., Wu, C.F.J.: Measuring location effects from factorial experiments with a directional response. Int. Stat. Rev. 63, 345–363 (1995)

    Article  MATH  Google Scholar 

  • Figueiredo, A.: Classificação de variáveis no contexto de um modelo probabilístico definido na n-esfera. Tese de Doutoramento, Faculdade de Ciências, Universidade de Lisboa (2000)

  • Figueiredo, A., Gomes, P.: Comparação dos parâmetros direccionais de k populações de Bingham. In: Carvalho, L., Brilhante, F., Rosado, F. (eds.) Novos rumos em Estatística, pp. 227–234. Edições SPE, Lisboa (2002)

    Google Scholar 

  • Figueiredo, A.: Two-way analysis of variance for data from a concentrated bipolar Watson distribution. J. Appl. Stat. 33, 575–581 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  • Figueiredo, A.: Multisample likelihood ratio tests based on bipolar Watson distributions defined on the hypersphere. Commun. Stat. Theory Methods 36, 1–6 (2007)

    MathSciNet  Google Scholar 

  • Figueiredo, A.: Two-way ANOVA for the Watson distribution. Stat. Pap. 49, 363–376 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  • Gomes, P., Figueiredo, A.: A new probabilistic approach for the classification of normalised variables. Bull. Int. Stat. Inst. LVIII(1), 403–404 (1999)

    Google Scholar 

  • Harrison, D., Kanji, G.K., Gadsden, R.J.: Analysis of variance for circular data. J. Appl. Stat. 13, 123–138 (1986)

    Article  Google Scholar 

  • Harrison, D., Kanji, G.K.: The development of analysis of variance for circular data. J. Appl. Stat. 15, 197–224 (1988)

    Article  Google Scholar 

  • Huo, V.: Small samples from Bingham distributions. PhD Thesis, University of Minnesota (1984)

  • Li, K.-H., Wong, C.K.-F.: Random sampling from the Watson distribution. Commun. Stat. Simul. 22(4), 997–1009 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  • Mardia, K.V., Jupp, P.E.: Directional Statistics. Wiley, Chichester (2000)

    MATH  Google Scholar 

  • Stephens, M.A.: Use of the von Mises distribution to analyse continuous proportions. Biometrika 69(1), 197–203 (1982)

    Article  MathSciNet  Google Scholar 

  • Stephens, M.A.: On Watson’s ANOVA for directions. In: Mardia K.V. (ed.) Art of Statistical Science, pp. 75–85 (1992)

  • Underwood, A.J., Chapman, M.G.: Multifactorial analyses of directions of movement of animals. J. Exp. Mar. Biol. Ecol. 91, 17–43 (1985)

    Article  Google Scholar 

  • Watson, G.S.: Analysis of dispersion on a sphere. Monthly Notices Roy. Astr. Soc.: Geophys. Suppl. 7, 153–159 (1956)

    Google Scholar 

  • Watson, G.S., Williams, E.J.: On the construction of significance tests on the circle and the sphere. Biometrika 43, 344–352 (1956)

    MATH  MathSciNet  Google Scholar 

  • Watson, G.S.: Statistics on Spheres. Wiley, New York (1983)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculdade de Economia/LIAAD, Universidade do Porto, Rua Dr. Roberto Frias, 4200-464, Porto, Portugal

    Adelaide Figueiredo

Authors
  1. Adelaide Figueiredo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Adelaide Figueiredo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Figueiredo, A. Multi-sample tests for axial data from Watson distributions. AStA Adv Stat Anal 93, 371–386 (2009). https://doi.org/10.1007/s10182-009-0114-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10182-009-0114-5

Keywords

Search

Navigation