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) have described some applications and addressed distributional problems through Monte Carlo simulation, deriving close to exact significance test points for a range of sample values. But there remain advantages to algebraic approximations to the exact distribution in relaxing restrictions on significance levels or sample sizes and permitting evaluation of ?P-values?. This paper examines two approaches. One is a simple adjustment to the asymptotic distribution (Feller, 1951) that improves its tail accuracy greatly for realistic sample size. The order is an approximation to the whole distribution, suitable for ?P-value? calculation, which is also reasonably precise in the tail. The Harrison and Treacy values and Monte Carlo simulation are used to confirm accuracy.