Hostname: page-component-7dd5485656-zlgnt Total loading time: 0 Render date: 2025-11-02T21:46:42.444Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

Extract

Let ξ 1 , 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 (ξ 1, ξ 2 , ···, ξm), that is, Fm (x) is defined as the number of variables ≦x divided by m.

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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