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Biometrika 1976 63(1):127-132; doi:10.1093/biomet/63.1.127
© 1976 by Biometrika Trust
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Sufficient statistics associated with a two-state second-order Markov chain

BENJAMIN KEDEM

Department of Mathematics, University of Maryland College Park

Statistical inference for binomial processes with second-order Markov dependence is worked out. Sufficient statistics for the 22 parameters associated with the process are found and their exact joint distribution is given in a closed form. An algorithm for finding the probability of k successes in n dependent trials is developed and a simple estimation procedure is suggested and applied to a meteorological time series.

Key Words: Binary data • Maximum likelihood • Meteorological time series • Second-order Markov chain • Sufficient statistics


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