Approximating the distribution of the R/s statistic

The R/s statistic, used for many years in hydrology, is increasingly employ ed in economics, although deficiencies in knowledge about its exact distrib ution have inhibited progress. Harrison and Treacy (1997) described some ap plications where R/s arises as a test statistic and they derived close to e xact critical values for conventional (5 per cent etc.) significance levels for a range of sample values through Monte Carlo simulation. This paper ex amines two approaches. One is a simple adjustment to the asymptotic distrib ution that improves its upper tail accuracy greatly and the other is an app roximation to the whole distribution, easily computed and suitable for "P-v alue" calculation, which is also reasonably precise in the upper tail. The Harrison and Treacy values and Monte Carlo simulation are used to confirm a ccuracy.