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

b) density f (x) = 1

(g)bg x g−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.