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An operation which inverts Bernoulli multiplication and associated stationary reversible Markov processes

Published online by Cambridge University Press:  14 July 2016

R. P. Littlejohn*
Affiliation:
MAF Technology
*
Postal address: MAF Technology, Invermay Agricultural Centre, Private Bag, Mosgiel, New Zealand.

Abstract

A simple operation is described which inverts Bernoulli multiplication. It is used to define two classes of stationary reversible Markov processes with general marginal distribution. These are compared to the DAR(1) process of Jacobs and Lewis (1978). LJAR(1) is used to model ovulation rate time series.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1992 

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References

Alzaid, A. and Al-Osh, M. (1988) First-order integer-valued autoregressive (INAR(1)) process: distributional and regression properties. Statist. Neerlandica 42, 5361.Google Scholar
Jacobs, P. A. and Lewis, P. A. W. (1978) Discrete time series generated by mixtures. I. Correlational and run properties. J. R. Statist. Soc. B40, 94105.Google Scholar
Jacobs, P. A. and Lewis, P. A. W. (1983) Stationary discrete autoregressive moving average time series generated by mixtures. J. Time Series Anal. 4, 1936.Google Scholar
Lewis, P. A. W. (1985) Some simple models for continuous variate time series. Water Resources Bull. 21, 635644.Google Scholar
Littlejohn, R. P. (1990a) Mutually reversible stationary Markovian time series models for non-negative marginal distributions with atoms at zero.Google Scholar
Littlejohn, R. P. (1992) Discrete minification processes and reversibility. J. Appl. Prob. 29, 8291.Google Scholar
McKenzie, E. (1988) Some ARMA models for dependent sequences of Poisson counts. Adv. Appl. Prob. 20, 822835.Google Scholar
Montgomery, G. W., Scott, I. C. and Johnstone, P. D. (1988) Seasonal changes in ovulation rate in Coopworth ewes maintained at different liveweights. Animal Reproduction Sci. 17, 197205.Google Scholar