Abstract
The first three sections (§§ 5, 6, 7) of this chapter cover basic theory. The last three (§§ 8, 9, 10) discuss applications in demography, medicine, biology and physics. If you are primarily interested in the sample mean and sample standard deviation, skip from § 7 directly to § 18.
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References
For the derivation, which depends upon Stirling’s formula see W. Feller, Introduction to Probability Theory, Vol. 1, Wiley (New York) 1957.
Another solution consists in transforming the h-axis so that the standard deviation of the transformed h becomes almost independent of p. See R. Rao, Advanced Statistical Methods in Biometric Research, Wiley (New York) 1952, pp. 207–214.
F. Wegmann, Die operative Behandlung der Bronchektasien, Diss. Zürich 1955, Zusammenfassung p. 39.
A curve which illustrates the shape of the error probability as a function of p in the limiting case of a rare event is shown in my note “Vertrauensgrenzen für unbekannte Wahrscheinlichkeiten”, Sitzungsber. sächs. Akad. Wiss. 91 (1939) p.213.
C. J. Clopper and E. S. Pearson, Biometrika 26 (1934), p. 404.
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© 1969 Springer-Verlag Berlin Heidelberg
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van der Waerden, B.L. (1969). Probabilities and Frequencies. In: Mathematical Statistics. Die Grundlehren der mathematischen Wissenschaften, vol 156. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-22137-2_3
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DOI: https://doi.org/10.1007/978-3-662-22137-2_3
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