Question: Negative binomial. Let X, Y be independently distributed according to negative binomial distributions N b(p1, m) and N b(p2, n) respectively, and let qi =

Negative binomial. Let X, Y be independently distributed according to negative binomial distributions N b(p1, m) and N b(p2, n) respectively, and let qi = 1 − pi .

(i) There exists a UMP unbiased test for testing H : θ = q2/q1 ≤ θ0 and hence in particular H : p1 ≤ p2.

(ii) Determine the conditional distribution required for testing H when m = n = 1.

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