Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-14T13:22:54.190Z Has data issue: false hasContentIssue false
  • English
  • Français

An exponential moving-average sequence and point process (EMA1)

Published online by Cambridge University Press:  14 July 2016

A. J. Lawrance  and
P. A. W. Lewis
A. J. Lawrance
Affiliation:
University of Birmingham
P. A. W. Lewis
Affiliation:
Naval Postgraduate School, Monterey, California
Get access Rights & Permissions [Opens in a new window]

Abstract

A construction is given for a stationary sequence of random variables {Xi} which have exponential marginal distributions and are random linear combinations of order one of an i.i.d. exponential sequence {εi}. The joint and trivariate exponential distributions of Xi−1, Xi and Xi+ 1 are studied, as well as the intensity function, point spectrum and variance time curve for the point process which has the {Xi} sequence for successive times between events. Initial conditions to make the point process count stationary are given, and extensions to higher-order moving averages and Gamma point processes are discussed.

Keywords

POINT PROCESSEXPONENTIAL INTERVALSCORRELATED EXPONENTIAL SEQUENCEMOVING AVERAGE STRUCTURESPECTRUM OF COUNTSBIVARIATE EXPONENTIAL DISTRIBUTIONCONDITIONAL CORRELATIONSTATIONARY INITIAL CONDITIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 1 , March 1977 , pp. 98 - 113
Copyright
Copyright © Applied Probability Trust 1977 

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

Downton, F. (1970) Bivariate exponential distributions of reliability theory. J. R. Statist. Soc. B 32, 408–417.Google Scholar
Cox, D. R. and Lewis, P. A. W. (1966) The Statistical Analysis of Series of Events. Methuen, London; Wiley, New York.CrossRefGoogle Scholar
Gaver, D. P. and Lewis, P. A. W. (1977) First-order autoregressive Gamma sequences and point processes. To appear.Google Scholar
Jacobs, P. A. and Lewis, P. A. W. (1977) A mixed autoregressive moving-average exponential sequence and point process (EARMA 1,1). Adv. Appl. Prob. 9, 87–104.CrossRefGoogle Scholar
Lawrance, A. J. (1972) Some models for stationary series of univariate events. In Stochastic Point Processes, ed. Lewis, P. A. W., Wiley, New York, 199–256.Google Scholar
Lawrance, A. J. (1976) On conditional and partial correlation. Amer. Statistician 30 (3), 146–149.Google Scholar