Skip to main content
SpringerLink
Log in

Modified Branching Process and Saddlepoint Approximations

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

This article presents a brief on using a saddlepoint approximations technique to solve some branching process problems; this method of approximation provides a good understanding of branching process behaviors such as probability density, mass function, and cumulative distribution function based on a moment generating function for complicated models such as nuclear chain reaction, survival of family name problems, and extinction probability problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. H. E. Daniels, ‘‘Saddlepoint approximations in statistics,’’ Ann. Math. Stat. 25, 631–650 (1954).

    Article  MathSciNet  Google Scholar 

  2. H. E. Daniels, ‘‘Tail probability approximations,’’ Int. Stat. Rev. 55, 37–48 (1987).

    Article  MathSciNet  Google Scholar 

  3. R. Lugannani and S. Rice, ‘‘Saddle point approximation for the distribution of the sum of independent random variables,’’ Adv. Appl. Probab. 12, 475–490 (1980).

    Article  MathSciNet  Google Scholar 

  4. N. Reid, ‘‘Saddlepoint methods and statistical inference,’’ Stat. Sci. 3, 213–227 (1988).

    MathSciNet  MATH  Google Scholar 

  5. E. Ronchetti, ‘‘Small sample asymptotics: A review with applications to robust statistics,’’ Comput. Statist. Data Anal. 10, 207–223 (1990).

    Article  MathSciNet  Google Scholar 

  6. R. W. Butler, Saddlepoint Approximations with Applications, Vol. 22 of Cambridge Series in Statistical and Probabilistic Mathematics (Cambridge Univ. Press, Cambridge, 2007).

  7. A. O. Al Mutairi and H. C. Low, ‘‘\(p\)-value for two-sample linear rank tests using permutation simulations and the normal approximation method,’’ Commun. Stat. Simul. Comput. 44, 819–826 (2015).

    Article  Google Scholar 

  8. A. O. Al Mutairi and H. C. Low, ‘‘Improved measures of the spread of data for some unknown complex distributions using saddlepoint approximations,’’ Commun. Stat. Simul. Comput. 45, 33–47 (2016).

    Article  MathSciNet  Google Scholar 

Download references

Funding

This research was supported financially by Taibah University, Medina, Saudi Arabia. The author thank the referee for constructive comments.

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Taibah University, 41521, Medina, Saudi Arabia

    Alya Al Mutairi

Authors
  1. Alya Al Mutairi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alya Al Mutairi.

Additional information

(Submitted by A. I. Volodin)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Al Mutairi, A. Modified Branching Process and Saddlepoint Approximations. Lobachevskii J Math 42, 404–407 (2021). https://doi.org/10.1134/S1995080221020153

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080221020153

Keywords:

Search

Navigation