Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-18T12:20:44.949Z Has data issue: false hasContentIssue false
  • English
  • Français

Normal approximations to discrete unimodal distributions

Published online by Cambridge University Press:  24 August 2016

B. G. Quinn  and
H. L. MacGillivray
B. G. Quinn*
Affiliation:
University of Queensland
H. L. MacGillivray*
Affiliation:
University of Queensland
*
∗Postal address: Department of Mathematics, University of Queensland, St. Lucia, QLD 4067, Australia.
∗Postal address: Department of Mathematics, University of Queensland, St. Lucia, QLD 4067, Australia.
Get access Rights & Permissions [Opens in a new window]

Abstract

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

Keywords

BIRTH-DEATH PROCESSHYPERGEOMETRIC DISTRIBUTIONSTRONGLY UNIMODAL DISTRIBUTIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 23 , Issue 4 , December 1986 , pp. 1013 - 1018
Copyright
Copyright © Applied Probability Trust 1986 

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

Barbour, A. D. (1974) On a functional central limit theorem for Markov population processes. Adv. Appl. Prob. 6, 21–39.CrossRefGoogle Scholar
Bartlett, M. S. (1960) Stochastic Population Models. Methuen, London.Google Scholar
Diamond, P. M. (1983) Functional response and some stationary distributions of searching parasites. Pure Mathematics Preprint 70, University of Queensland.Google Scholar
Feller, W. (1950) An Introduction to Probability Theory and its Applications, Vol. 1. Wiley, New York.Google Scholar
Karlin, S. (1968) Total Positivity, Vol. 1. Stanford University Press, Stanford, CA.Google Scholar
Mcneil, D. R. and Schach, S. (1973) Central limit analogues for Markov population processes. J.R. Statist. Soc. B 35. 1–23.Google Scholar
Moran, P. A. P. (1968) An Introduction to Probability Theory. Clarendon Press, Oxford.Google Scholar
Moran, P. A. P. (1979) Asymptotic analysis and local lattice central limit theorems. J. Appl. Prob. 16, 541–553.Google Scholar