Approximating the distribution of Greenwood's statistic

摘要

textabstractStatistics based on uniform spacings are often used in goodness‐of‐fit problems. In this paper special attention is paid to the distribution of Greenwood's statistic. Although its asymptotic distribution is normal, the normal approximation is extremely bad, even for large sample sizes. It is shown that the Edge‐worth expansion yields a considerably better approximation for the distribution of this statistic. Furthermore, an overview is given of the higher order asympto‐tics for the sum of functions of uniform spacings, of which Greenwood's statistic is a special case. Copyright