Hostname: page-component-89b8bd64d-dvtzq Total loading time: 0 Render date: 2026-05-06T21:21:42.718Z Has data issue: false hasContentIssue false
  • English
  • Français

AN ASYMPTOTIC EXPANSION FOR THE INSPECTION PARADOX

Published online by Cambridge University Press:  12 December 2005

J. E. Angus
J. E. Angus
Affiliation:
School of Mathematical Sciences, Claremont Graduate University, Claremont, CA 91711, E-mail: john.angus@cgu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Suppose that there are n families with children attending a certain school and that the number of children in these families are independent and identically distributed random variables, each with probability mass function P{X = j} = pj, j ≥ 1, with finite mean μ = [sum ]j≥1 jpj. If a child is selected at random from the school and XI is the number of children in the family to which the child belongs, it is known that limn→∞ P{XI = j} = jpj /μ,j ≥ 1. Here, asymptotic expansions for P{XI = j} are developed under the condition E|X|3 < ∞.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 1 , January 2006 , pp. 87 - 94
Copyright
© 2006 Cambridge University Press

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

REFERENCES

Angus, J.E. (1997). The inspection paradox inequality. SIAM Review 39: 95–97.Google Scholar
Brown, B.M. (1970). Characteristic functions, moments, and the central limit theorem. Annals of Mathematical Statistics 41(2): 658–664.Google Scholar
Hall, P. & Heyde, C.C. (1980). Martingale limit theory and its applications. New York: Academic Press.
Hu, T. & Zhuang, W. (2004). Likelihood ratio ordering of the inspection paradox. Probability in the Engineering and Informational Sciences 18: 503–510.Google Scholar
Ross, S.M. (2000). Introduction to probability models, 7th ed. New York: Academic Press.
Ross, S.M. (2003). The inspection paradox. Probability in the Engineering and Informational Sciences 17: 47–51.Google Scholar
Stirzaker, D. (1997). Elementary probability. Cambridge: Cambridge University Press.