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Negative Association Does not Imply Log-Concavity of the Rank Sequence

Published online by Cambridge University Press:  14 July 2016

Klas Markström*
Affiliation:
Umeå University
*
Postal address: Department of Mathematics and Mathematical Statistics, Umeå University, SE-901 87 Umeå, Sweden. Email address: klas.markstrom@math.umu.se
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Abstract

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We present a minimum counterexample to the conjecture that a negatively associated random variable has an ultra-log-concave rank sequence. The rank sequence does not in fact even need to be unimodal.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 2007 

References

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[3] Pemantle, R. (2000). Towards a theory of negative dependence. Probabilistic techniques in equilibrium and nonequilibrium statistical physics. J. Math. Phys. 41, 13711390.Google Scholar