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Negative binomial exponential family

For fixed positive integer

r

, the failures-before-the-

r

th-success distribution is a one-parameter exponential family with

θ = lo g (1 - p) < 0, T (x) = x, A (θ) = - r lo g (1 - e^{θ}),

and carrier

h (x) = (x x + r - 1)

.

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