Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-06-02T00:56:57.383Z Has data issue: false hasContentIssue false
  • English
  • Français

The supremum distribution of another Gaussian process

Published online by Cambridge University Press:  14 July 2016

Noel Cressie  and
Robert W. Davis
Noel Cressie*
Affiliation:
The Flinders University of South Australia
Robert W. Davis*
Affiliation:
The Flinders University of South Australia
*
∗Postal address: School of Mathematical Sciences, The Flinders University of South Australia, Bedford Park, SA 5042, Australia.
∗Postal address: School of Mathematical Sciences, The Flinders University of South Australia, Bedford Park, SA 5042, Australia.
Get access Rights & Permissions [Opens in a new window]

Abstract

A formula is derived for the supremum of a stationary Gaussian process which has a correlation function that is tent-like in shape, until it flattens out at a constant negative value. Examples and graphs are presented in the last section.

Keywords

NEGATIVE CORRELATIONSTATIONARY GAUSSIAN PROCESSSUPREMUM DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 131 - 138
Copyright
Copyright © 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

Bhattacharya, P. and Brockwell, P. (1976) The minimum of an additive process with applications to signal estimation and storage theory. Z. Wahrscheinlichkeitsth. 37, 51–75.Google Scholar
Birnbaum, Z. (1975) Testing for intervals of increased mortality. In Reliability and Fault Tree Analysis, ed. Singpurvalla, N., SIAM, Philadelphia, 413–426.Google Scholar
Cressie, N. (1977) On some properties of the scan statistic on the circle and the line. J. Appl. Prob. 14, 272–283.Google Scholar
Cressie, N. (1980) The asymptotic distribution of the scan statistic under uniformity. Ann. Prob. 8, 828–840.Google Scholar
Karlin, S. and Mcgregor, J. (1959) Coincidence probabilities. Pacific J. Math. 9, 1141–1164.Google Scholar
Naus, J. (1966a) Some probabilities, expectations and variances for the size of largest clusters and smallest intervals. J. Amer. Statist. Assoc. 61, 1191–1199.Google Scholar
Naus, J. (1966b) A power comparison of two tests of non random clustering. Technometrics 8, 493–517.Google Scholar
Orear, J. and Cassel, D. (1971) Applications of statistical inference to physics. In Foundations of Statistical Inference, ed. Godambe, V. and Sprott, D., Holt, Rinehart, and Winston, Toronto, 280–288.Google Scholar
Saunders, I. (1978) Locating bright spots in a point process. Adv. Appl. Prob. 10, 587–612.Google Scholar
Scheid, F. (1968) Schaum's Outline of Theory and Problems of Numerical Analysis. McGraw-Hill, New York.Google Scholar
Shepp, L. (1971) First passage time for a particular Gaussian process. Ann. Math. Statist. 42, 946–951.Google Scholar
Shepp, L. and Slepian, D. (1976) First passage time for a particular stationary periodic Gaussian process. J. Appl. Prob. 13, 27–38.Google Scholar