Question

5. Consider the gamma distribution and recall that its mean and variance are μ-αβ and σ2-032, respectively. Assume a is known. Let X1, . . , X,, ~ X where X ~ f(x; α, β). is strict. your findings to verify the additivity property in(3) = n1(3). you computed V(An). Relate V(ßn) and In(3). interval to estimate T (a) Compute the Fisher information I(8) of A (why?) and examine whether the Cramer-Rao inequality (b) Find the score of the sample and compute the Fisher information In() of the sample directly. Use (c) Fron Problem 4 of Hw5 you know that the maximum likelihood estimator, ' of β is unbiased and (d) Let τ sinh,3. Use , the Delta method, and asymptotic normality to find the (l-a) confidence

Answer 1

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