This module contains quite a bit of Calculus manipulations. This problem assesses your mathematical problem solving...

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This module contains quite a bit of Calculus manipulations. This problem assesses your mathematical problem solving for obtaining MOM estimator and MLE, asymptotic distribution, and confidence interval. Submit to Canvas a pdf scan of your solutions to this problem. The Pareto distribution has a pdf f (x | xm, ) -a-1 = xmx ; x xm, > 1. This distribution is named after the 19th century Italian economist Vilfredo Pareto. It sees application in actuarial science and geology where heavy-tailed skewed distributions are needed. Suppose m > 0 is fixed and we have a random sample X,..., Xn iid Pareto (a). Find the MOM and MLE for a, the asymptotic variance of the MLE, and a confidence interval for a using the asymptotic distribution of the MLE. Present derivations for the mathematical formulations of these four items. Also, fit this Pareto model to the following data. The output should have four pieces: MOM estimate, MLE estimate, asymptotic variance estimate, and confidence interval. claims = The following are 40 wind-related catastrophes in 1977 with claims of at least $2 million dollars. So the Pareto distribution cut off is m = 2. Values are in millions of dollars. # claims in millions of dollars c(2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,5,5,5,5,6,6,6,6,8,8,9,15,17,22,23,24,24,25,27,32,43) This module contains quite a bit of Calculus manipulations. This problem assesses your mathematical problem solving for obtaining MOM estimator and MLE, asymptotic distribution, and confidence interval. Submit to Canvas a pdf scan of your solutions to this problem. The Pareto distribution has a pdf f (x | xm, ) -a-1 = xmx ; x xm, > 1. This distribution is named after the 19th century Italian economist Vilfredo Pareto. It sees application in actuarial science and geology where heavy-tailed skewed distributions are needed. Suppose m > 0 is fixed and we have a random sample X,..., Xn iid Pareto (a). Find the MOM and MLE for a, the asymptotic variance of the MLE, and a confidence interval for a using the asymptotic distribution of the MLE. Present derivations for the mathematical formulations of these four items. Also, fit this Pareto model to the following data. The output should have four pieces: MOM estimate, MLE estimate, asymptotic variance estimate, and confidence interval. claims = The following are 40 wind-related catastrophes in 1977 with claims of at least $2 million dollars. So the Pareto distribution cut off is m = 2. Values are in millions of dollars. # claims in millions of dollars c(2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,5,5,5,5,6,6,6,6,8,8,9,15,17,22,23,24,24,25,27,32,43)