Stochastic dominance, which is based on the comparison of distribution functions, is one of the most popular preference measures. However, its use is limited to the case where the goal is to compare pairs of distribution functions, whereas in many cases it is interesting to compare sets of distribution functions: this may be the case for instance when the available information does not allow to fully elicitate the probability distributions of the random variables. To deal with these situations, a number of generalisations of the notion of stochastic dominance are proposed; their connection with an equivalent p-box representation of the sets of distribution functions is studied; a number of particular cases, such as sets of distributions associated to possibility measures, are investigated; and an application to the comparison of the Lorenz curves of countries within the same region is presented.
Stochastic dominance with imprecise information
Ignacio Montes,Enrique Miranda,S. Montes
Published 2014 in Computational Statistics & Data Analysis
ABSTRACT
PUBLICATION RECORD
- Publication year
2014
- Venue
Computational Statistics & Data Analysis
- Publication date
2014-03-01
- Fields of study
Mathematics, Computer Science
- Identifiers
- External record
- Source metadata
Semantic Scholar
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EXTRACTION MAP
CLAIMS
CONCEPTS
- countries within the same region
The group of countries used as the empirical comparison set in the application.
Aliases: same-region countries
- imprecise information
Incomplete information that does not allow the probability distribution of a random variable to be fully elicited.
Aliases: uncertain information
- lorenz curve
A curve used to describe inequality and compare the distribution of a quantity across countries.
Aliases: Lorenz curves
- p-box representation
A probability-box representation that encodes a set of admissible distribution functions through lower and upper bounds.
Aliases: probability box representation, p-box
- possibility measure
A non-additive uncertainty measure used here to define a special class of distribution sets.
Aliases: possibility measures
- set of distribution functions
A collection of candidate cumulative distribution functions used to represent incomplete probabilistic information.
Aliases: sets of distributions, set of distributions
- stochastic dominance
A preference criterion based on comparing distribution functions to rank uncertain outcomes.
Aliases: stochastic dominances
REFERENCES
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