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. Harrison and Treacy (1997) described some applications where R/s arises as a test statistic and they derived close to exact critical values for conventional (5 per cent etc.) significance levels for a range of sample values through Monte Carlo simulation. This paper examines two approaches. One is a simple adjustment to the asymptotic distribution that improves its upper tail accuracy greatly and the 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 and Monte Carlo simulation are used to confirm accuracy.