Given [MATH] l_1(u,v)=\int_{-\infty}^{+\infty}|U-V| [/MATH] the 1-Wasserstein distance with [MATH]u[/MATH] and [MATH]v[/MATH] two probability distributions and [MATH]U[/MATH] and [MATH]V[/MATH] their respective CDFs. The values of [MATH]u[/MATH] and [MATH]v[/MATH] are all positive in my case.
Let's assume that I have already computed [MATH]a=max(u)[/MATH], [MATH]b=max(v)[/MATH], [MATH]c=min(u)[/MATH], and [MATH]d=min(v)[/MATH],
Does [MATH] l_1 [/MATH]have an upper and a lower bound?
Let's assume that I have already computed [MATH]a=max(u)[/MATH], [MATH]b=max(v)[/MATH], [MATH]c=min(u)[/MATH], and [MATH]d=min(v)[/MATH],
Does [MATH] l_1 [/MATH]have an upper and a lower bound?
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