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An application of chain-dependent processes to meteorology

Published online by Cambridge University Press:  14 July 2016

Richard W. Katz
Richard W. Katz*
Affiliation:
National Center for Atmospheric Research*, Boulder, Colorado
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Abstract

An explicit formula is derived for the variance normalizing constant in the central limit theorem for chain-dependent processes. As an application to meteorology, a specific chain-dependent process is proposed as a probabilistic model for the sequence of daily amounts of precipitation. This model is a generalization of the commonly used Markov chain model for the occurrence of precipitation.

Keywords

CHAIN-DEPENDENT PROCESSMARKOV CHAINPROBABILITY MODELMETEOROLOGY
Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 3 , September 1977 , pp. 598 - 603
Copyright
Copyright © Applied Probability Trust 1977 

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References

Denzel, G. E. and O'brien, G. L. (1975) Limit theorems for extreme values of chain-dependent processes. Ann. Prob. 3, 773–779.Google Scholar
Gabriel, K. R. and Neumann, J. (1962) A Markov chain model for daily rainfall occurrence at Tel Aviv. Quart. J. R. Meteor. Soc. 88, 90–95.Google Scholar
Ibragimov, I. A. (1962) Some limit theorems for stationary processes. Theory Prob. Appl. 7, 349–382.Google Scholar
Katz, R. W. (1974) A Stochastic Process Defined on a Markov Chain: Properties and an Application to Meteorology. Ph.D. dissertation, Pennsylvania State University.Google Scholar
Katz, R. W. (1977) Precipitation as a chain-dependent process. J. Appl. Meteor. To appear.Google Scholar
Keilson, J. and Wishart, D. M. G. (1964) A central limit theorem for processes defined on a finite Markov chain. Proc. Camb. Phil. Soc. 60, 547–567.Google Scholar
Kemeny, J. G. and Snell, J. L. (1960) Finite Markov Chains. Van Nostrand, Princeton.Google Scholar
Loynes, R. M. (1965) Extreme values in uniformly mixing stationary stochastic processes. Ann. Math. Statist. 36, 993–999.Google Scholar
Mises, R. Von (1936) La distribution de la plus grande de n valeurs. Reprinted in Selected Papers 2, 271–294, American Mathematical Society, Providence (1954).Google Scholar
Neyman, J. and Scott, E. L. (1967) Some outstanding problems relating to rain modification. Proc. 5th Berkeley Symp. Math. Statist. Prob. 5, 293–326.Google Scholar
O'brien, G. L. (1974) Limit theorems for sums of chain-dependent processes. J. Appl. Prob. 11, 582–587.Google Scholar
Resnick, S. I. and Neuts, M. F. (1970) Limit laws for maxima of a sequence of random variables defined on a Markov chain. Adv. Appl. Prob. 2, 323–340.CrossRefGoogle Scholar
Todorovic, P. and Woolhiser, D. A. (1975) A stochastic model of n-day precipitation. J. Appl. Meteor. 14, 17–24.Google Scholar