The behavioral meaning of the median
Author | |
---|---|
Keywords | |
Abstract |
We extend the notion of statistical preference to the general framework of imprecise probabilities, by proposing a new notion of desirability of gambles called sign-desirability , different from the usual desirability notion in Walley s framework. We axiomatically characterize coherent families of sign-desirable gambles. We furthermore prove that the pair of lower and upper previsions of a gamble, according to this new desirability notion, coincides with the pair of bounds (infimum and supremum) of the set of medians associated to a coherent family of linear previsions. Thus, a general notion of median is naturally derived, and provided with a behavioral meaning. As a consequence of these results, the connection between statistical preference in classical Probability Theory, and the sign of the median of the difference of two random variables is laid bare.
|
Year of Publication |
2015
|
Journal |
Information Sciences
|
Volume |
294
|
Number of Pages |
127-138
|
ISSN Number |
0020-0255
|
URL |
http://www.sciencedirect.com/science/article/pii/S0020025514008548
|
DOI |
10.1016/j.ins.2014.08.049
|
Download citation | |
Notes |
Innovative Applications of Artificial Neural Networks in Engineering
|
Notes |
Innovative Applications of Artificial Neural Networks in Engineering |