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2. Let X₁, X2,..., Xn be iid random variables from a Pareto distribution, with cdf F(x; a) = 1-xa, x ≥ 1, a > 0. A. Find the Cramer-Rao lower bound for estimators of a. B. Show that the MLE for a is ân n ΣIn X₂ C. Construct an estimator T(ân) such that E(T(ân)) = a. Is it a best estimator for a?

2. Let X₁, X2,..., Xn be iid random variables from a Pareto distribution, with cdf F(x; a) = 1-xa, x ≥ 1, a > 0. A. Find the Cramer-Rao lower bound for estimators of a. B. Show that the MLE for a is ân n ΣIn X₂ C. Construct an estimator T(ân) such that E(T(ân)) = a. Is it a best estimator for a?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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2. Let X₁, X2,..., Xn be iid random variables from a Pareto distribution, with cdf F(x; a) = 1-xa, x ≥ 1, a > 0. A. Find the Cramer-Rao lower bound for estimators of a. B. Show that the MLE for a is an n Σ', la XT C. Construct an estimator T(ân) such that E(T(ân)) = a. Is it a best estimator for a?
Transcribed Image Text:2. Let X₁, X2,..., Xn be iid random variables from a Pareto distribution, with cdf F(x; a) = 1-xa, x ≥ 1, a > 0. A. Find the Cramer-Rao lower bound for estimators of a. B. Show that the MLE for a is an n Σ', la XT C. Construct an estimator T(ân) such that E(T(ân)) = a. Is it a best estimator for a?
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