Hostname: page-component-5c6d5d7d68-wbk2r Total loading time: 0 Render date: 2024-08-16T16:17:09.801Z Has data issue: false hasContentIssue false

Extended criterion for comparison of empirical distributions

Published online by Cambridge University Press:  14 July 2016

Ora Engleberg Percus
Affiliation:
City University of New York
Jerome K. Percus
Affiliation:
Courant Institute of Mathematical Sciences, New York University

Abstract

A generating function technique is used to determine the probability that the deviation between two empirical distributions drawn from the same population lies within a given band a specified number of times. We also treat the asymptotic problem of very large sample size, and obtain explicit expressions when the relative number of failures is very small or very large.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 

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.)

References

[1] Smirnov, N. V. (1939) Sur les écarts de la courbe de distribution comprique. Recueil Math. New Series 6 (98), 326.Google Scholar
[2] Gnedenko, B. V. and Rvaceva, E. L. (1952) On a problem of the comparison of two empirical distributions (in Russian). Dokl. Akad. Nauk. SSSR 82, 513516.Google Scholar
[3] Takács, L. (1962) Ballot problems. Z. Wahrscheinlichkeitsth. 1, 154158.CrossRefGoogle Scholar
[4] Percus, O. E. and Percus, J. K. (1969) On the distribution of the number of zero partial sums. J. Appl. Prob. 6, 162176.CrossRefGoogle Scholar
[5] Percus, O. E. and Percus, J. K. (1970) Random walk and the comparison of two empirical distributions. To be published in SIAM J. Appl. Math. 18.CrossRefGoogle Scholar
[6] Whittaker, E. T. and Watson, G. N. (1952) A Course in Modern Analysis. Cambridge U.P. 132133.Google Scholar
[7] Engelberg, O. (1965) On some problems concerning a restricted random walk. J. Appl. Prob. 2, 396404.CrossRefGoogle Scholar
[8] Magnus, W. and Oberhettinger, F. (1954) Formulas and Theorems for the Functions of Mathematical Physics. Chelsea Publishing Co. 9899.Google Scholar