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Abstract
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Wasserstein distances provide a metric on a space of probability measures. We consider the space
of all probability
measures on the finite set
,
where
is a positive integer. The 1-Wasserstein distance,
, is a function
from
to
.
This paper derives closed-form expressions for the first and second moments of
on
assuming a uniform
distribution on
.
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Keywords
Wasserstein, earth mover, probability simplex, simplex,
standard simplex, moments, expected value, variance
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Mathematical Subject Classification 2010
Primary: 28A33, 60B05
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Milestones
Received: 12 December 2019
Revised: 8 September 2020
Accepted: 29 September 2020
Published: 9 April 2021
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