A General formula for the upper tail significance levels of empirical distribution function test statistics

In this paper ve obtain an asymptotic expression for the upper tail area of the distribution of an infinite weighted sum of chi-square random variables and show how this can be applied to distributions of various goodness of fit test statistics. Results obtained by this general approach are comparable with those reported previously in the literature. In the case of the Cramer-von Mises statistic an empirical adjustment is given vhich significantly improves on previous approximations. For the Kuiper statistic the corresponding empirical adjustment leads to an existing highly accurate approximation.