Why the 1-Wasserstein distance is the area between the two marginal CDFs

Autor:	De Angelis, Marco, Gray, Ander
Rok vydání:	2021
Předmět:	Mathematics - Statistics Theory Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	We elucidate why the 1-Wasserstein distance $W_1$ coincides with the area between the two marginal cumulative distribution functions (CDFs). We first describe the Wasserstein distance in terms of copulas, and then show that $W_1$ with the Euclidean distance is attained with the $M$ copula. Two random variables whose dependence is given by the $M$ copula manifest perfect (positive) dependence. If we express the random variables in terms of their CDFs, it is intuitive to see that the distance between two such random variables coincides with the area between the two CDFs. Comment: 6 pages, 1 figure, a pedagogical note
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2111.03570 Zobrazit plný text záznamu View this record from Arxiv