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Biometrika 1971 58(2):357-368; doi:10.1093/biomet/58.2.357
© 1971 by Biometrika Trust
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A definition of independence for bounded-sum, nonnegative, integer-valued variables

J. N. DARROCH

Flinders University of South Australia

Consider two nonnegative variables whose sum is constrained to be less than or equal to n. By the usual definition of independence, these two variables virtually have to be dependent because of the constraint. In this paper the definition of independence is modified to allow for the constraint. Only integer-valued variables are considered. Following the bivariate theory of what is termed F-independence, a multivariate theory is developed.

Key Words: Dependence due to a constraint • Bounded-sum variables • Independence • F-independence • Multivariate independence • Maximum entropy • Multinomial • Multihypergeometric


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