GAUSS-LAGUERRE DYNAMICS - AN EFFICIENT METHOD OF COMPUTING INTEGRALS IN MULTIPLE COMPARISONS

Computing with Gauss-Laguerre quadratures is a common practice when computing the distribution of the studentized version of many statistics used in normal theory multiple comparisons. We study the dynamics of the points associated with such quadrature and apply the results to the simple example of the studentized maximum modulus. Because most distributions used in multiple comparisons require relatively expensive numerical quadrature for evaluation of their non-studentized integrand, the efficiency of the suggested method is clear as it requires fewer integrand evaluations than the standard Gauss-Laguerre quadrature.