#StackBounty: #statistical-significance #threshold #bhattacharyya Thresholds for Bhattacharyya coefficient – when do the distributions …

Bounty: 50

The Bhattacharyya coefficient of two discrete probability distributions is defined as
$$
BC(p,q) = sum_{i=1}^n sqrt{p_iq_i}.
$$

This coefficient lies within the interval $[0,1]$ and if $p=q$ then it is 1 as
$$
sum_{i=1}^n sqrt{p_i^2} = sum_{i=1}^n p_i = 1.
$$

Thus values lower than 1 might indicate that $p$ and $q$ differ. Are there any thresholds derived in the literature or significance tests that give guidance when we can accept the hypothesis that $p$ and $q$ differ?


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