Talk:Lévy–Prokhorov metric
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mistake on "Relation to other distances" section
[edit]The second bullet point apparently is wrong. I tried to find out that result in page 175 in Rachev and nothing similar seems to be there. Furthermore the probabilities <math> \gamma=(1-\alpha) \delta_a+\alpha \delta_0$<math> with <math>0<a<\alpha<1<math>, and <math>\delta_0<math> seem to provide a contradiction to such statement, since <math>W_p(\gamma, \delta_0)^p=a^p\alpha<math> and <math>\pi(\gamma, \delta_0)=a <math>, it is easy to find <math>a, \alpha<math> and <math>p<math> such that <math>a^p\alpha-a^2<0<math>, contradicting the statement. Luiscc1900 (talk) 16:57, 3 November 2022 (UTC)
- I agree with this. I also checked the source and the cited inequality is nowhere to be seen! I am not 100% sure about the correctness of your counterexample (I think in the definition of $\gamma$ you need to swap $\alpha$ and $1-\alpha$ as weights), but I agree with the conclusion. 129.19.63.105 (talk) 20:33, 1 April 2024 (UTC)