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Suppose we have a sample y from the model f(y; , ) = / (y / )^(1 )e ( y/ )^ for y > 0.
Suppose we have a sample y from the model f(y; , ) = / (y / )^(1 )e ( y/ )^ for y > 0. Assume = 1 is fixed and use 0 as the true value of (Choose it yourself). Use a simulation study to calculate the point estimate of . You must use MME, MLE and Bayes with an Exponential prior for such that a priori, E() = 0. Use the mode of the posterior density as the Bayes point estimate. Show graphically the maximum of the likelihood on the likelihood function as well as the mode of the posterior.
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