# #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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