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An investigation by high speed sampling of the frequency distribution of rank correlation

Eine Untersuchung der Frequenzverteilung der Rang Korrelation

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Summary

The functionϕ n (S) is linearly related tof n (r), the frequency distribution ofSpearman's coefficient for rank correlation. Exact combinatorial results forn≦8 and an asymptotic approximation are available inKendall [3].

Since the combinatorial approach is intractable forn>10 the principal purpose of this paper was to studyϕ n (S) forn>10 by the Monte Carlo method. The conclusion was reached that the asymptotic approximation is satisfactory forn>20.

Zusammenfassung

Die Funktionϕ n (S) hängt linear mitf n (r), der Verteilung desSpearmanschen Rangkorrelationskoeffizienten zusammen. Exakte Ergebnisse fürn≦8 und eine asymptotische Näherung sind inKendall [3], zu finden.

Da exakte Werte fürn>10 wegen des Rechenaufwands schwer zu erhalten sind, ist es das hauptsächliche Ziel dieses Artikels,ϕ n (S) fürn>10 mit einem Monte-Carlo-Verfahren zu berechnen. Wir sehen, daß die asymptotische Näherung fürn>20 ausreichend genau ist.

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References

  1. Durstenfeld, R.: Collected Algorithms from CACM, p. 235. San Diego, California: General Atomic. 1964.

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  2. Hall, M. Jr., andD. Knuth: Combinatorial Analysis and Computers (Part 2). Amer. Math.M 72, 21 (1965).

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  3. Kendall, M.: The Advanced Theory of Statistics, Vol. 1, 2nd ed., p. 388. London: Charles Griffin and Co. 1958.

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Authors and Affiliations

  1. Department of Industrial Engineering, Auburn University, 36830, Auburn, AL, U.S.A.

    S. Maghsoodloo

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  1. S. Maghsoodloo
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Maghsoodloo, S. An investigation by high speed sampling of the frequency distribution of rank correlation. Computing 8, 1–12 (1971). https://doi.org/10.1007/BF02234038

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  • DOI: https://doi.org/10.1007/BF02234038

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