Realizable Monotonicity and Inverse Probability Transform

James Allen Fill and Motoya Machida
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James Allen Fill: The Johns Hopkins University, Department of Mathematical Sciences
Motoya Machida: Utah State University, Department of Mathematics and Statistics

A chapter in Distributions With Given Marginals and Statistical Modelling, 2002, pp 63-71 from Springer

Abstract: Abstract Abstract A system (P α : α ∈ A) of probability measures on a common state space S indexed by another index set A can be “re al ized” by a system (X α : α ∈ A) of Svalued random variables on some probability space in such a way that each X α is distributed as P α. Assuming that A and S are both partially ordered, we may ask when the system (P α : α E A) can be realized by a system (X α : α ∈ A) with the monotonicity property that X α ≤ Xβ almost surely whenever α≤ β. When such a realization is possible, we call the system (P α : α ∈ A) “realizably monotone.” Such a system necessarily is stochastically monotone, that is, satisfies P α

Keywords: Realizable monotonicity; stochastic monotonicity; monotonicity equivalence; perfect sampling; partially ordered set; Strassen’s theorem; marginal problem; inverse probability transform; synchronizing function; synchronizable; Primary 62E05; secondary 06A06; 60J10; 05C05; 05C38 (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-94-017-0061-0_8

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