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1 results

  • Pareto processes

  • Hsiaw-Chan Yeh, Barry C. Arnold, Christopher A. Robertson
  • Journal:
    Journal of Applied Probability / Volume 25 / Issue 2 / June 1988
    Published online by Cambridge University Press:
    14 July 2016, pp. 291-301
    Print publication:
    June 1988

  • 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.