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Minification processes and their transformations

Published online by Cambridge University Press:  14 July 2016

Peter A. W. Lewis  and
Ed McKenzie
Peter A. W. Lewis*
Affiliation:
Naval Postgraduate School
Ed McKenzie*
Affiliation:
University of Strathclyde
*
∗Postal address: Department of Operations Research, Naval Postgraduate School, Monterey, CA 93940, USA.
∗∗Postal address: Department of Statistics, University of Strathclyde, Glasgow, UK.
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Abstract

It is shown that the stationary, autoregressive, Markovian minification processes introduced by Tavares and Sim can be extended to give processes with marginal distributions other than the exponential and Weibull distributions. Necessary and sufficient conditions on the hazard rate of the marginal distributions are given for a minification process to exist. Results are given for the derivation of the autocorrelation function; these correct the expression for the Weibull given by Sim. Monotonic transformations of the minification processes are also discussed and generate a whole new class of autoregressive processes with fixed marginal distributions. Stationary processes generated by a maximum operation are also introduced and a comparison of three different Markovian processes with uniform marginal distributions is given.

Keywords

TIME SERIESEAR(1)TRANSFORMATIONSMAXIMUM PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 1 , March 1991 , pp. 45 - 57
Copyright
Copyright © Applied Probability Trust 1991 

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