Realizable monotonicity and inverse probability transform

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dc.creatorFill, James Allen
dc.creatorMachida, Motoya
dc.date2000-10-03
dc.date.accessioned2026-07-07T04:37:48Z
dc.date.available2026-07-07T04:37:48Z
dc.descriptionA system (P_a: a in A) of probability measures on a common state space S indexed by another index set A can be ``realized'' by a system (X_a: a in A) of S-valued random variables on some probability space in such a way that each X_a is distributed as P_a. Assuming that A and S are both partially ordered, we may ask when the system (P_a: a in A) can be realized by a system (X_a: a in A) with the monotonicity property that X_a <= X_b almost surely whenever a <= b. When such a realization is possible, we call the system (P_a: a in A) ``realizably monotone.'' Such a system necessarily is stochastically monotone, that is, satisfies P_a <= P_b in stochastic ordering whenever a <= b. In general, stochastic monotonicity is not sufficient for realizable monotonicity. However, for some particular choices of partial orderings in a finite state setting, these two notions of monotonicity are equivalent. We develop an inverse probability transform for a certain broad class of posets S, and use it to explicitly construct a system (X_a: a in A) realizing the monotonicity of a stochastically monotone system when the two notions of monotonicity are equivalent.
dc.descriptionPresented at "Distributions with Given Marginals and Statistical Modelling," Barcelona, Spain, July 17-20, 2000. See also http://www.mts.jhu.edu/~fill/ and http://www.math.usu.edu/~machida/
dc.identifierhttps://arxiv.org/abs/math/0010026
dc.identifierhttp://arxiv.org/abs/math/0010026
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60040
dc.subjectProbability
dc.subjectCombinatorics
dc.subject60E05 (primary), 06A06, 60J10, 05C05, 05C38 (secondary)
dc.titleRealizable monotonicity and inverse probability transform
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