This problem will look at some details and extensions of the calculation in Example 10.1.18.
(a) Reproduce Figure 10.1.1, calculating the ARE for known β. (You can follow the calculations in Example A.0.7, or do your own programming.)
(b) Verify that the ARE(,) comparison is the same whether β is known or unknown.
(c) For estimation of β with known μ, show that the method of moment estimate and MLEs are the same. (It may be easier to use the (α, β) parameterization.)
(d) For estimation of β with unknown μ, the method of moment estimate and MLEs are not the same. Compare these estimates using asymptotic relative efficiency, and produce a figure like Figure 10.1.1, where the different curves correspond to different values of μ.
Figure 10.1.1

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ARE 10 Gamma mean