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

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