Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T06:29:45.352Z Has data issue: false hasContentIssue false
  • English
  • Français

The distribution and moments of the number of components of a random function

Published online by Cambridge University Press:  14 July 2016

Joseph Kupka
Joseph Kupka*
Affiliation:
Monash University
*
∗Postal address: Department of Mathematics, Monash University, Clayton, VIC 3168, Australia.
Get access Rights & Permissions [Opens in a new window]

Abstract

A relatively simple formula is presented for the probability distribution of the number K of components of a random function. This formula facilitates the (computer) calculation of the factorial moments of K and yields new expressions for the mean and variance of K.

Keywords

CYCLIC ELEMENTSFACTORIAL MOMENTS
Type
Short Communications
Information
Journal of Applied Probability , Volume 27 , Issue 1 , March 1990 , pp. 202 - 207
Copyright
Copyright © Applied Probability Trust 1990 

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] Feller, W. (1968) Introduction to Probability Theory and Its Applications, Vol. 1, 3rd edn. Wiley, New York.Google Scholar
[2] Folkert, J. E. (1955) The Distribution of the Number of Components of a Random Mapping Function. Ph.D. Dissertation, Michigan State University.Google Scholar
[3] Harris, B. (1960) Probability distributions related to random mappings. Ann. Math. Statist. 31, 1045–1062.Google Scholar
[4] Katz, L. (1955) Probability of indecomposability of a random mapping function. Ann. Math. Statist. 26, 512–517.CrossRefGoogle Scholar
[5] Kolchin, V. F. A problem of the allocation of particles in cells and random mappings. Theory Prob. Appl. 21, 48–63.CrossRefGoogle Scholar
[6] Ross, S. M. (1981) A random graph. J. Appl. Prob. 18, 309–315.Google Scholar
[7] Rubin, H. and Sitgreaves, R. (1954) Probability distributions related to random transformations on a finite set. Tech. Report No. 19A, Applied Mathematics and Statistics Laboratory, Stanford University.Google Scholar
[8] Wilson, R. J. (1985) Introduction to Graph Theory, 3rd edn. Longman, Harlow.Google Scholar