Recurrence Relations Among Moments of Order Statistics from Two Related Outlier Models

It is shown that the moments of order statistics in samples drawn from a continuous population with pdf f(x) symmetric about zero comprising a single outlier with pdf g(x) symmetric about zero can be expressed in terms of the moments of order statistics in samples drawn from the population obtained by folding the pdf f(x) at zero and the moments of order statistics in samples drawn from the population obtained by folding the pdf f(x) at zero comprising a single outlier with pdf obtained by folding g(x) at zero. The cumulative round off error involved in numerical evaluation of the moments of order statistics from the symmetric-outlier model, using a table of the moments of order statistics from the folded population and the moments of order statistics from the folded-outlier model, is not serious.