The Maximum Relative Error in the Filliben Approximation for Uniform Order Statistic Medians
Kenneth A. Snyder
The relative error of the Filliben [Technometrics, 17, 111, 1975] approximation for uniform order statistic medians is calculated from the ratio of the error to the mean spacing between medians. The true uniform order statistic medians were calculated by numerical integration using extended precision representations for numbers. An asymptotic analysis from sample sizes up to 100 000 demonstrates that the relative error has an absolute maximum of approximately 1.6 %. For the probability plot correlation coefficient test, this is also the maximum relative error in the order statistic medians of the test distribution.
correlation coeffieient, Filliben test, order statistic medians, probability plot