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Stochastic dominance is a partial order between random variables. [1] [2] It is a form of stochastic ordering.The concept arises in decision theory and decision analysis in situations where one gamble (a probability distribution over possible outcomes, also known as prospects) can be ranked as superior to another gamble for a broad class of decision-makers.
Stochastic dominance relations are a family of stochastic orderings used in decision theory: [1] Zeroth-order stochastic dominance: A ≺ ( 0 ) B {\displaystyle A\prec _{(0)}B} if and only if A ≤ B {\displaystyle A\leq B} for all realizations of these random variables and A < B {\displaystyle A<B} for at least one realization.
The test does not identify where this stochastic dominance occurs or for how many pairs of groups stochastic dominance obtains. For analyzing the specific sample pairs for stochastic dominance, Dunn's test, [4] pairwise Mann–Whitney tests with Bonferroni correction, [5] or the more powerful but less well known Conover–Iman test [5] are ...
Ranking gambles by mean-preserving spreads is a special case of ranking gambles by second-order stochastic dominance – namely, the special case of equal means: If B is a mean-preserving spread of A, then A is second-order stochastically dominant over B; and the converse holds if A and B have equal means.
The Kruskal-Wallis test is designed to detect stochastic dominance, so the null hypothesis is the absence of stochastic dominance. Using multi-modal distributions you can quickly generate counter examples to the claim "the null hypothesis of the Kruskal-Wallis is equal distribution of the samples".
Stochastic dominance; This page was last edited on 14 April 2023, at 05:18 (UTC). Text is available under the Creative Commons Attribution-ShareAlike 4.0 ...
The presence of marginal conditional stochastic dominance is sufficient, but not necessary, for a portfolio to be inefficient. This is because marginal conditional stochastic dominance only considers incremental portfolio changes involving two sub-groups of assets—one whose holdings are decreased and one whose holdings are increased.
This requires a stochastic ordering on the lotteries. Several such orderings exist; the most common in social choice theory, in order of strength, are DD (deterministic dominance), BD (bilinear dominance), SD (stochastic dominance) and PC (pairwise-comparison dominance). See stochastic ordering for definitions and examples.