Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-28T21:16:59.437Z Has data issue: false hasContentIssue false
  • English
  • Français

Orthant probabilities and Gaussian Markov processes

Published online by Cambridge University Press:  14 July 2016

P. A. P. Moran
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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