Hellinger Distance - Examples

Examples

The squared Hellinger distance between two normal distributions and is:

H^2(P, Q) = 1 - \sqrt{\frac{2\sigma_1\sigma_2}{\sigma_1^2+\sigma_2^2}} \, e^{-\frac{1}{4}\frac{(\mu_1-\mu_2)^2}{\sigma_1^2+\sigma_2^2}}.

The squared Hellinger distance between two exponential distributions and is:

H^2(P, Q) = 1 - \frac{2 \sqrt{\alpha \beta}}{\alpha + \beta}.

The squared Hellinger distance between two Weibull distributions and (where is a common shape parameter and are the scale parameters respectively):

H^2(P, Q) = 1 - \frac{2 (\alpha \beta)^{k/2}}{\alpha^k + \beta^k}.

The squared Hellinger distance between two Poisson distributions with rate parameters and, so that and, is:

H^2(P,Q) = 1-e^{-\frac{1}{2}(\sqrt{\alpha} - \sqrt{\beta})^2}.

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