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Orthant probabilities and Gaussian Markov processes

Published online by Cambridge University Press:  14 July 2016

P. A. P. Moran
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Abstract

A method is given for calculating the probability that n terms of a Gaussian first-order autoregressive series lie between any specified limits where n may be as large as 20 or more.

Keywords

AUTOREGRESSIVE PROCESSES
Type
Part 7—Algorithms and Computations
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 413 - 417
Copyright
Copyright © 1986 Applied Probability Trust 

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References

Gehrlein, W. V. (1979) A representation for quadrivariate normal positive orthant probabilities. Commun. Statist. B Simulation and computation B8, 349–358.Google Scholar
Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.Google Scholar
Johnson, N. L. and Kotz, S. (1972) Distributions in Statistics: Continuous Multivariate Distributions. Wiley, New York.Google Scholar
Longuet-Higgins, M. S. (1963) Bounding approximations to the distribution of intervals between zeros of a stationary Gaussian process. Proc. Symp. Time Series Analysis , ed. Rosenblatt, M. Wiley, New York.Google Scholar
Plackett, R. L. (1954) A reduction formula for normal multivariate integrals. Biometrika 41, 351–360.Google Scholar
Slepian, D. (1963) On the zeros of Gaussian noise. Proc. Symp. Time Series Analysis , ed. Rosenblatt, M. Wiley, New York.Google Scholar