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  "body": "\n## Summary\n\nThe Hellinger distance is a distance between two probability distributions.\nIt compares the square roots of their densities in the $L^2$ sense.\nIt takes values in $[0, 1]$ and behaves well under independent products.\nIt is a standard tool in asymptotic statistics, for example for rates of convergence of estimators and in testing.\n\n## Explanations\n\n### L1 human\n\nTake the square roots of two density functions, so that each becomes a unit vector in a space of functions.\nThe Hellinger distance measures how far apart these two unit vectors are.\nTwo equal distributions have distance $0$, and two distributions that live on disjoint sets have distance $1$.\nFor instance, a fair coin and a coin that always shows heads have squared Hellinger distance $1 - 1/\\sqrt{2} \\approx 0.29$.\n[[Total variation distance|3SZESKX3N5]] is another common distance, and the two are always comparable.\n",
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