|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'585
Articles rated: 2609
25 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Realizable monotonicity and inverse probability transform | | James Allen Fill
; Motoya Machida
; | | Date: |
3 Oct 2000 | | Subject: | Probability; Combinatorics MSC-class: 60E05 (primary), 06A06, 60J10, 05C05, 05C38 (secondary) | math.PR math.CO | | Affiliation: | Johns Hopkins Univ.), Motoya Machida (Utah State Univ. | | Abstract: | A 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. | | Source: | arXiv, math.PR/0010026 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER