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.
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REFERENCES
H. E. Daniels, ‘‘Saddlepoint approximations in statistics,’’ Ann. Math. Stat. 25, 631–650 (1954).
H. E. Daniels, ‘‘Tail probability approximations,’’ Int. Stat. Rev. 55, 37–48 (1987).
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).
N. Reid, ‘‘Saddlepoint methods and statistical inference,’’ Stat. Sci. 3, 213–227 (1988).
E. Ronchetti, ‘‘Small sample asymptotics: A review with applications to robust statistics,’’ Comput. Statist. Data Anal. 10, 207–223 (1990).
R. W. Butler, Saddlepoint Approximations with Applications, Vol. 22 of Cambridge Series in Statistical and Probabilistic Mathematics (Cambridge Univ. Press, Cambridge, 2007).
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).
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).
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This research was supported financially by Taibah University, Medina, Saudi Arabia. The author thank the referee for constructive comments.
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(Submitted by A. I. Volodin)
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Al Mutairi, A. Modified Branching Process and Saddlepoint Approximations. Lobachevskii J Math 42, 404–407 (2021). https://doi.org/10.1134/S1995080221020153
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DOI: https://doi.org/10.1134/S1995080221020153