Approximating the Distribution of the R/s statistic

The R/s statistic, used for many years in hydrology, is increasingly employed in economics,although deficiencies in knowledge about its exact distribution have inhibited progress. Harrisonand Treacy (1997) described some applications where R/s arises as a test statistic and they derivedclose to exact critical values for conventional (5 per cent etc.) significance levels for a range ofsample values through Monte Carlo simulation. This paper examines two approaches. One is asimple adjustment to the asymptotic distribution that improves its upper tail accuracy greatly andthe other is an approximation to the whole distribution, easily computed and suitable for 'P-value' calculation, which is also reasonably precise in the upper tail. The Harrison and Treacy values andMonte Carlo simulation are used to confirm accuracy.