Skip to main content
SpringerLink
Log in

Characterizations of multivariate spherical distributions inl ∞-norm

  • Published:
Test Aims and scope Submit manuscript

Abstract

The objective of this work is to characterize families of distributions which consist of mixtures of the uniform distributions on the surface of the N-sphere in thel ∞-norm. We discuss the characterization through distribution functions and stochastic representations rather than through a measure theoretic approach. Connections with the finite forms of de Finetti-type theorems are considered.

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

  • Barlow, R. (1991). De Finetti's le prévision: ses lois logiques, ses sources subjectives.In Breakthroughs in Statistics. Johnson, N.; Kotz, S. (editors). Springer.

  • Barlow, R. and M. Mendel (1992). De Finetti-type representations for life distributions.Journal of the American Statistical Association,8, 1116–1122.

    Article  MathSciNet  Google Scholar 

  • Barlow, R. and F. Spizzichino (1993). Schur-concave survival functions and survival analysis.Journal of Computational and Applied Mathematics,46, 437–447.

    Article  MathSciNet  Google Scholar 

  • Barlow, R. and P. Tsai (1995). Foundational issues concerning the analysis of censored data.Lifetime Data Analysis,1, 27–34.

    Article  MathSciNet  Google Scholar 

  • de Finetti, B. (1937). La prévision: ses lois logiques, ses sources subjectives.Annales del Institute Henry Poincaré,7, 1–68.

    Google Scholar 

  • de Finetti, B. (1949). Le vraie et le probable.Dialectica,3, 78–92.

    MathSciNet  Google Scholar 

  • Diaconis, P. and D. Freedman (1980). Finite exchangeable sequences.Annals of Probability,8, 745–764.

    MathSciNet  Google Scholar 

  • Diaconis, P. and D. Freedman (1984). Partial exchangeability and sufficiency. In proceedings of the Indian Statistical Institute Golden Jubilee International Conference on Statistics: Applications and New Directions. Calcutta, 205–236.

  • Diaconis, P. and D. Freedman (1987). A dozen de Finetti-style results in search of a theory.Annales del Institute Henry Poincaré,23, 397–423.

    MathSciNet  Google Scholar 

  • Diaconis, P., M. Eaton. and S. Lauritzen (1992). Finite de Finetti theorems in linear models and multivariate analysis.Scandinavian Journal of Statistics,19, 289–315.

    MathSciNet  Google Scholar 

  • Eaton, M. (1981). On the projections of isotropic distributions.Annals of Statistics,9, 391–400.

    MathSciNet  Google Scholar 

  • Fang, K. T., S. Kotz and K.W. Ng (1990).Symmetric multivariate and related distributions. London New-York: Chapman and Hall.

    MATH  Google Scholar 

  • Hayakawa, Y. (1993). Inter-relationships betweenl p -isotropic densities andl q -isotropic survival functions, and de Finetti representations of Schur-concave survival functions.Australian Journal of Statistics,35, 3, 327–332.

    MathSciNet  Google Scholar 

  • Iglesias, P., F. Matus, C.A.B. Pereira and N.I. Tanaka (1996). On finite sequences conditionally uniform given minima and maxima. In preparation.

  • Iglesias, P. (1993). Finite forms of de Finetti's Theorem: A predictivistic approach to statistical inference in finite populations (In Portuguese). Doctoral Thesis. Instituto de Matemática e Estatística, Universidade de São Paulo.

  • Kingman, J.F.C. (1972). On random sequences with spherical symmetry.Biometrika,59, 183–197.

    Article  MathSciNet  Google Scholar 

  • Osiewalski, J. and M.F. Steel (1993). Robust inference inl q -spherical models.Biometrika,80, 2, 456–60.

    MathSciNet  Google Scholar 

  • Rachev, S.T. and L. Rüschendorf (1991). Approximate Independence of Distributions on Spheres and their Stability Properties.Annals of Probabability 19, 1311–1337.

    Google Scholar 

  • Ressel, P. (1985). de Finetti-type theorems: an analytic approach.Annals of Probability,13, 898–922.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Estadística, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile

    Pilar L. Iglesias

  2. IME/USP, Caixa Postal 66281, 05315-970, São Paulo, Brazil

    Carlos A. B. Pereira & Nelson I. Tanaka

Authors
  1. Pilar L. Iglesias
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carlos A. B. Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nelson I. Tanaka
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Partially supported by DIUC, Fundación Andes/C-12777/9 and CNPq

Rights and permissions

Reprints and permissions

About this article

Cite this article

Iglesias, P.L., Pereira, C.A.B. & Tanaka, N.I. Characterizations of multivariate spherical distributions inl ∞-norm. Test 7, 307–324 (1998). https://doi.org/10.1007/BF02565115

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02565115

Key Words

AMS subject classification

Search

Navigation