Hostname: page-component-7b7567c8c-7pwfn Total loading time: 0 Render date: 2026-11-12T18:32:36.362Z Has data issue: false hasContentIssue false
  • English
  • Français

Pareto processes

Published online by Cambridge University Press:  14 July 2016

Hsiaw-Chan Yeh,
Barry C. Arnold and
Christopher A. Robertson
Hsiaw-Chan Yeh*
Affiliation:
National Taiwan University
Barry C. Arnold*
Affiliation:
National Taiwan University
Christopher A. Robertson*
Affiliation:
University of California, Riverside
*
∗ Postal address: Department of Finance, National Taiwan University, 21 Hsu-Chow Road, Taipei, Taiwan 10020, Republic of China.
∗∗ Postal address: Department of Statistics, University of California, Riverside, CA 92521, USA.
∗∗ Postal address: Department of Statistics, University of California, Riverside, CA 92521, USA.
Get accessRights & Permissions [Opens in a new window]

Abstract

An autoregressive process ARP(1) with Pareto-distributed inputs, analogous to those of Lawrance and Lewis (1977), (1980), is defined and its properties developed. It is shown that the stationary distributions are Pareto. Further, the maximum and minimum processes are asymptotically Weibull, and the ARP(1) process is shown to be closed under maximization or minimization when the number of terms is geometrically distributed. The ARP(1) process leads naturally to an extremal process in the sense of Lamperti (1964). Statistical inference for the ARP(1) process is developed. An absolutely continuous variant of the Pareto process is described.

Keywords

AUTOREGRESSIVE PROCESSBIVARIATE PARETO DISTRIBUTIONSEXTREMAL PROCESSESGEOMETRIC MINIMA

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 2 , June 1988, pp. 291 - 301
Copyright
Copyright © Applied Probability Trust 1988 

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.)

Article purchase

Temporarily unavailable

References

Arnold, B. C. (1983) Pareto Distributions. International Cooperative Publishing House, Fairland, Maryland.Google Scholar
Dwass, M. (1964) Extremal processes. Ann. Math. Statist. 35, 1718–1725.CrossRefGoogle Scholar
Fletcher, R. and Powell, M. J. D. (1963) A rapid descent method for minimization. Computer J. 6(2), 163–168.Google Scholar
Johnson, N. L. and Kotz, S. (1970) Distributions in Statistics: Continuous, Univariate Distributions , Vol. I. Wiley, New York.Google Scholar
Lamperti, J. (1964) On extreme order statistics. Ann. Math. Statist. 35, 1726–1737.Google Scholar
Lawrance, A. J. and Lewis, P. A. W. (1977) An exponential moving average sequence and point process. J. Appl. Prob. 14, 98–113.CrossRefGoogle Scholar
Lawrance, A. J. and Lewis, P. A. W. (1980) The exponential autoregressive-moving average EARMA(p, q) process J.R. Statist. Soc. B 42, 150–161.Google Scholar
Yeh-Shu, H. C. (1983) Pareto Processes. Unpublished Ph.D. dissertation, University of California, Riverside.Google Scholar