### Abstract

Distance correlation is a relatively new measure of dependence in probability theory and statistics, which has the great advantage that it gives zero if and only if the variables are independent. In this paper we define its possibilistic version. Namely, we equip each γ -level set of the joint possibility distribution with a uniform probability distribution, then we determine the probabilistic distance covariance and correlation between the marginal distributions. Finally, the possibilistic distance covariance and correlation is computed as the weighted average of these probabilistic measures of dependence.

Language | English |
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Title of host publication | Studies in Computational Intelligence |

Publisher | Springer Verlag |

Pages | 175-181 |

Number of pages | 7 |

DOIs | |

Publication status | Published - Jan 1 2019 |

### Publication series

Name | Studies in Computational Intelligence |
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Volume | 796 |

ISSN (Print) | 1860-949X |

### Fingerprint

### Keywords

- Dependence
- Distance correlation
- Distance covariance
- Fuzzy numbers
- Possibilistic correlation

### ASJC Scopus subject areas

- Artificial Intelligence

### Cite this

*Studies in Computational Intelligence*(pp. 175-181). (Studies in Computational Intelligence; Vol. 796). Springer Verlag. https://doi.org/10.1007/978-3-030-00485-9_20

**On possibilistic version of distance covariance and correlation.** / Harmati, István; Fullér, R.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Studies in Computational Intelligence.*Studies in Computational Intelligence, vol. 796, Springer Verlag, pp. 175-181. https://doi.org/10.1007/978-3-030-00485-9_20

}

TY - CHAP

T1 - On possibilistic version of distance covariance and correlation

AU - Harmati, István

AU - Fullér, R.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Distance correlation is a relatively new measure of dependence in probability theory and statistics, which has the great advantage that it gives zero if and only if the variables are independent. In this paper we define its possibilistic version. Namely, we equip each γ -level set of the joint possibility distribution with a uniform probability distribution, then we determine the probabilistic distance covariance and correlation between the marginal distributions. Finally, the possibilistic distance covariance and correlation is computed as the weighted average of these probabilistic measures of dependence.

AB - Distance correlation is a relatively new measure of dependence in probability theory and statistics, which has the great advantage that it gives zero if and only if the variables are independent. In this paper we define its possibilistic version. Namely, we equip each γ -level set of the joint possibility distribution with a uniform probability distribution, then we determine the probabilistic distance covariance and correlation between the marginal distributions. Finally, the possibilistic distance covariance and correlation is computed as the weighted average of these probabilistic measures of dependence.

KW - Dependence

KW - Distance correlation

KW - Distance covariance

KW - Fuzzy numbers

KW - Possibilistic correlation

UR - http://www.scopus.com/inward/record.url?scp=85054733181&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054733181&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-00485-9_20

DO - 10.1007/978-3-030-00485-9_20

M3 - Chapter

T3 - Studies in Computational Intelligence

SP - 175

EP - 181

BT - Studies in Computational Intelligence

PB - Springer Verlag

ER -