Title | The behavioral meaning of the median |

Publication Type | Journal Article |

Year of Publication | 2015 |

Authors | Couso, Inés, Moral Serafín, and Sánchez Luciano |

Journal | Information Sciences |

Volume | 294 |

Pagination | 127 - 138 |

ISSN | 0020-0255 |

Keywords | Desirable gamble, Imprecise Probability, Median, Statistical preference, Stochastic ordering |

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. |

Notes | Innovative Applications of Artificial Neural Networks in Engineering |

URL | http://www.sciencedirect.com/science/article/pii/S0020025514008548 |

DOI | 10.1016/j.ins.2014.08.049 |