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Asymptotic Cumulants for Distributions of k-State Markov Chains

Published online by Cambridge University Press:  24 October 2008

P. V. Krishna Iyer  and
N. S. Shakuntala
P. V. Krishna Iyer
Affiliation:
Defence Science LaboratoryDelhi-6 (India)
N. S. Shakuntala
Affiliation:
Defence Science LaboratoryDelhi-6 (India)
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Extract

The expectation, variance and covariance for different states of a k-state Markov chain have been given by Patankar (6), Whittle (7), Good (3) and Bhat (l). Patankar's results involve the k latent roots of the determinantal equation. As it is not easy to determine the latent roots when k > 2, the actual asymptotic values of variances and covariances cannot be readily evaluated. Whittle gives exact probability distributions for the transitions, but the moments have been obtained after some gross approximations. Good (3) and Bhat(l) have given the first two moments and product moment for the frequency of different states. By using certain methods developed by Iyer and Kapur(4), the first four cumulants and product cumulants for the transition numbers of a two-state Markov chain were calculated and presented in an earlier publication(5).

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 2 , April 1962 , pp. 427 - 430
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

REFERENCES

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