ROBSCALE: RATS module to compute robust alternative to standard deviation
robscale.src computes a robust alternative to the standard deviation as a measure of scale (dispersion). The standard deviation is easily distorted by outliers and may therefore be quite misleading. robscale.src computes the Qn statistic of Rousseeuuw and Croux, which is very robust and also has good efficiency (relative to the standard deviation) when the data are in fact uncontaminated Gaussian random variables. (P. J. Rousseeuw and C. Croux, "Alternatives to the median absolute deviation," Journal of the American Statistical Association, Dec 1993, vol. 88, no. 424, pp. 1273-1283). Specifically, if the series x contains n observations, then there are n(n-1)/2 differences of the form abs( x(i)-x(j) ), i < j. when these differences are ranked, Qn is approximately the 25th percentile. the cost of computing Qn grows rapidly as n increases, but the Rousseeuw-Croux algorithm is very fast and needs relatively little computer memory and disk space. myseries is the univariate data from which Qn is to be computed. the first observation is nbeg and the last observation is nend.
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