The distribution of the square sum of Dirichlet random variables and a table with quantiles of Greenwood's statistic

2010/08/24 by Thomas Royen, Royen, Thomas
Computer Science · Decision Sciences · Mathematics · #62E15 #62H10 #Advanced Statistical Process Monitoring #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1008.4059

openalex publication_date 2010/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The exact distribution of the square sum of Dirichlet random variables is given by two different univariate integral representations. Alternatively, three representations by orthogonal series with Jacobi or Legendre polynomials are derived. As a special case the distribution of the square sum of spacings - also called Greenwood's statistic - is obtained. Nine quantiles of this statistic are tabulated with eight digits where the number of squares ranges from 10 to 100.

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