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Random Probability Measures with Given Mean and Variance

Journal of Theoretical Probability volume 15, pages 919–937 (2002)Cite this article

Abstract

This article describes several natural methods of constructing random probability measures with prescribed mean and variance, and focuses mainly on a technique which constructs a sequence of simple (purely discrete, finite number of atoms) distributions with the prescribed mean and with variances which increase to the desired variance. Basic properties of the construction are established, including conditions guaranteeing full support of the generated measures, and conditions guaranteeing that the final measure is discrete. Finally, applications of the construction method to optimization problems such as Plackett's Problem are mentioned, and to experimental determination of average-optimal solutions of certain control problems.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia, 30332

    Lisa Bloomer & Theodore P. Hill

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  1. Lisa Bloomer
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  2. Theodore P. Hill
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Correspondence to Theodore P. Hill.

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Bloomer, L., Hill, T.P. Random Probability Measures with Given Mean and Variance. Journal of Theoretical Probability 15, 919–937 (2002). https://doi.org/10.1023/A:1020688620366

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  • DOI: https://doi.org/10.1023/A:1020688620366

  • Random distribution
  • random homeomorphisms
  • random probability measures
  • variance split
  • variance split array