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Moments of the Mean of Dubins–Freedman Random Probability Distributions

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  • Pieter Allaart

    (University of North Texas)

Abstract

Explicit formulas are given to recursively generate the moments of the mean M for Dubins–Freedman random distribution functions with arbitrary base measure μ. Using a standard inversion formula for moments of a distribution on the unit interval, the distribution of M is approximated for several natural choices of μ. The support of the mean is also considered. It is shown that the support of M is connected whenever μ is concentrated on the vertical bisector of the unit square S, but may have arbitrarily many gaps otherwise.

Suggested Citation

  • Pieter Allaart, 2003. "Moments of the Mean of Dubins–Freedman Random Probability Distributions," Journal of Theoretical Probability, Springer, vol. 16(2), pages 471-488, April.
    • Handle: RePEc:spr:jotpro:v:16:y:2003:i:2:d:10.1023_a:1023582913550
    DOI: 10.1023/A:1023582913550
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    References listed on IDEAS

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    1. Lisa Bloomer & Theodore P. Hill, 2002. "Random Probability Measures with Given Mean and Variance," Journal of Theoretical Probability, Springer, vol. 15(4), pages 919-937, October.
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