Markov binomial distribution of order k and its applications

Markov binomial distribution of order k and its applications In this paper, we study the distribution of $$X_{n,k}^c $$ X n , k c , the number of occurrences of success runs of length k in the sequence of n Markov Binary Trials arranged on circle under four popular schemes of counting runs. Such distribution is referred as circular Markov binomial distribution of order k and is studied for the first time in this paper. The pgf of $$X_{n,k}^c $$ X n , k c is expressed in the form of matrix polynomial and an algorithm is developed to obtain the exact probability distribution. We include some numerical results in order to demonstrate feasibility and simplicity of the theoretical results developed. Further we discuss applications of the distribution of circular binomial run statistic $$X_{n,k}^c $$ X n , k c in studying the distribution of length of longest success run on circle and also in evaluation of circular reliability systems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Statistical Papers Springer Journals

Markov binomial distribution of order k and its applications

Loading next page...
 
/lp/springer_journal/markov-binomial-distribution-of-order-k-and-its-applications-i0T7TNAqmY
Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2016 by Springer-Verlag Berlin Heidelberg
Subject
Statistics; Statistics for Business/Economics/Mathematical Finance/Insurance; Probability Theory and Stochastic Processes; Economic Theory/Quantitative Economics/Mathematical Methods; Operations Research/Decision Theory
ISSN
0932-5026
eISSN
1613-9798
D.O.I.
10.1007/s00362-015-0728-5
Publisher site
See Article on Publisher Site

Abstract

In this paper, we study the distribution of $$X_{n,k}^c $$ X n , k c , the number of occurrences of success runs of length k in the sequence of n Markov Binary Trials arranged on circle under four popular schemes of counting runs. Such distribution is referred as circular Markov binomial distribution of order k and is studied for the first time in this paper. The pgf of $$X_{n,k}^c $$ X n , k c is expressed in the form of matrix polynomial and an algorithm is developed to obtain the exact probability distribution. We include some numerical results in order to demonstrate feasibility and simplicity of the theoretical results developed. Further we discuss applications of the distribution of circular binomial run statistic $$X_{n,k}^c $$ X n , k c in studying the distribution of length of longest success run on circle and also in evaluation of circular reliability systems.

Journal

Statistical PapersSpringer Journals

Published: Jan 8, 2016

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off