Again suppose that independent observations x, x2,..., n are available from the Pareto distribution with pdf...

 

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Again suppose that independent observations x₁, x2,..., n are available from the Pareto distribution with pdf B on x > 1, x+1 with > 0. You showed in Question 1 that the log-likelihood is f(x) = = n - l(B) = n log B (B+1) ►log xi i=1 and the MLE of 3 is B = n Σ1 log Xi It also turns out to be the case that n 3² E{-l" (B)} = In this question, interest lies in testing Ho: B = 1 against H₁: B 1. (a) Obtain formulae for both Wald statistics, W₁ and W2, in terms of (and n). (b) Show that the score statistic, S, can be written n S = (1-3)²2 32 (c) What common procedure would now be followed to complete each Wald or score test to obtain the appropriate p-value? [There is no need to carry out any calculations.] What is the justification for the distribution that is used? Again suppose that independent observations x₁, x2,..., n are available from the Pareto distribution with pdf B on x > 1, x+1 with > 0. You showed in Question 1 that the log-likelihood is f(x) = = n - l(B) = n log B (B+1) ►log xi i=1 and the MLE of 3 is B = n Σ1 log Xi It also turns out to be the case that n 3² E{-l" (B)} = In this question, interest lies in testing Ho: B = 1 against H₁: B 1. (a) Obtain formulae for both Wald statistics, W₁ and W2, in terms of (and n). (b) Show that the score statistic, S, can be written n S = (1-3)²2 32 (c) What common procedure would now be followed to complete each Wald or score test to obtain the appropriate p-value? [There is no need to carry out any calculations.] What is the justification for the distribution that is used?

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Ans fxBB x 0 Page1 B1 There are y independent observations ... View the full answer