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

摘要

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.