Negative dependence of independent random variables conditional on their total sum
نویسندگان
چکیده
Let X1,. .. , XN be independent non-negative integer valued random variables. In this paper we present a sufficient condition for the collection (X1,. .. , XN) to be stochastically increasing in the sum X1 + · · · + XN. Thus, if the condition is satisfied then (X1,. .. , XN) are negatively associated when conditioned on the sum X1 + · · · + XN. The result is a generalization of the main theorem in [8] by Liggett, and the proof is based on the coupling method. As an example, we also prove that a collection of independent Borel-distributed random variables are negatively associated when conditioned on their total sum.
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