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On the comparison of a theoretical and an empirical distribution function

Published online by Cambridge University Press:  14 July 2016

Lajos Takács
Lajos Takács*
Affiliation:
Case Western Reserve University
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Extract

Let ξ1, ξ2, ···, ξm be mutually independent random variables having a common distribution function P{ξr≦x} = F(x)(r = 1, 2, ···, m). Let Fm(x) be the empirical distribution function of the sample (ξ1, ξ2, ···, ξm), that is, Fm(x) is defined as the number of variables ≦x divided by m.

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 2 , June 1971 , pp. 321 - 330
Copyright
Copyright © Applied Probability Trust 1971 

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References

[1] Darling, D. A. (1960) On the theorems of Kolmogorov-Smirnov. Theor. Probability Appl. 5, 356–361.CrossRefGoogle Scholar
[2] Nef, W. (1964) Über die Differenz zwischen theoretischer und empirischer Verteilungsfunktion. Z. Wahrscheinlichkeitsth. 3, 154–162.CrossRefGoogle Scholar
[3] Smirnov, N. V. (1939) On deviations of the empirical distribution function. (In Russian) Mat. Sbornik 6, 3–26.Google Scholar
[4] Takács, L. (1967) Combinatorial Methods in the Theory of Stochastic Processes. John Wiley, New York.Google Scholar
[5] Takács, L. (1970) Combinatorial methods in the theory of order statistics. Proc. First Internat. Symp. on Nonparametric Techniques in Statistical Inference. Bloomington, Indiana, June 1–6, 1969. Cambridge University Press, 359–384.Google Scholar