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Exponential-family deviance ( $D (θ_{1}, θ_{2})$ )

The deviance from

θ_{1}

to

θ_{2}

is twice the Kullback-Leibler divergence:

D (θ_{1}, θ_{2}) = 2 E_{θ_{1}} [lo g \frac{f _{θ_{1}} ( Y )}{f _{θ_{2}} ( Y )}] .

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