Suppose X1,...,Xn are i.i.d. with the gamma (g, b) density f(x) = 1 (g)bg xg1 e x/b

Suppose X1,...,Xn are i.i.d. with the gamma Γ(g,

b) density f(x) = 1

Γ(g)bg xg−1 e

−x/b x > 0 , with both parameters unknown (and positive). Consider testing the null hypothesis that g = 1, i.e., under the null hypothesis the underlying density is exponential.

Determine the likelihood ratio test statistic and find its limiting distribution.