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Modified Bessel functions and their applications in probability and statistics

Author

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  • Robert, Christian

Abstract

Modified Bessel functions are often of use in the probabilistic and statistical analysis of spherical distributions and we give here the main properties of these functions. In particular, they appear in Bayes estimators with respect to uniform distributions on spheres; we derive a constructive result about the approximation of a Bayes estimator by a mixture of these primitive estimators.

Suggested Citation

  • Robert, Christian, 1990. "Modified Bessel functions and their applications in probability and statistics," Statistics & Probability Letters, Elsevier, vol. 9(2), pages 155-161, February.
  • Handle: RePEc:eee:stapro:v:9:y:1990:i:2:p:155-161
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    Cited by:

    1. Árpád Baricz & Dragana Jankov Maširević & Tibor K. Pogány, 2021. "Approximation of CDF of Non-Central Chi-Square Distribution by Mean-Value Theorems for Integrals," Mathematics, MDPI, vol. 9(2), pages 1-12, January.
    2. Marchand, Éric & Perron, François, 2005. "Improving on the mle of a bounded location parameter for spherical distributions," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 227-238, February.
    3. Marchand, Éric & Perron, François, 2002. "On the minimax estimator of a bounded normal mean," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 327-333, July.
    4. Andrés Martín & Ernesto Estrada, 2023. "Fractional-Modified Bessel Function of the First Kind of Integer Order," Mathematics, MDPI, vol. 11(7), pages 1-13, March.
    5. Jan Beran & Britta Steffens & Sucharita Ghosh, 2022. "On nonparametric regression for bivariate circular long-memory time series," Statistical Papers, Springer, vol. 63(1), pages 29-52, February.
    6. Fourdrinier, Dominique & Marchand, Éric, 2010. "On Bayes estimators with uniform priors on spheres and their comparative performance with maximum likelihood estimators for estimating bounded multivariate normal means," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1390-1399, July.

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