Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T07:23:37.545Z Has data issue: false hasContentIssue false
  • English
  • Français

A limiting distribution for Bernoulli trials with second-order Markov dependence

Published online by Cambridge University Press:  14 July 2016

Barron Brainerd
Barron Brainerd*
Affiliation:
University of Toronto
*
∗ Postal address: Department of Mathematics, University of Toronto, Toronto, M5S 1A1, Canada.
Get access Rights & Permissions [Opens in a new window]

Abstract

Let ℰ be an event governed by a homogeneous second-order two-state Markov chain. Assume the steady state has been achieved. Consider Nm the number of times that ℰ occurs in m successive trials. The limiting distribution of P(Nm = k) is obtained under the condition that mP(ℰ)=λ.

Keywords

SECOND-ORDER MARKOV CHAINSLIMITING DISTRIBUTIONPÓLYA-AEPPLI DISTRIBUTIONLAGUERRE FUNCTIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 2 , June 1983 , pp. 419 - 422
Copyright
Copyright © Applied Probability Trust 1983 

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] Brainerd, B. and Chang, S. M. (1983) The distribution of the number of ocurrences of an event governed by two state Markov chains of first and second order. Canad. J. Statist. 10, 225–231.CrossRefGoogle Scholar
[2] Patil, G. P. and Joshi, S. W. (1968) A Dictionary and Bibliography of Discrete Distributions. Hafner, New York.Google Scholar
[3] Rainville, E. D. (1960) Special Functions. Macmillan, New York.Google Scholar
[4] Wang, Y. H. (1981) On the limit of the Markov binomial distribution. J. Appl. Prob. 18, 937–942.CrossRefGoogle Scholar