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A random sample, X₁,..., Xn, is drawn from a Pareto population with pdf ого f(x0, v) = 20+1₁) (1), 0>0, v> 0. (a) Find the MLEs of 0 and v. (b) Show that the LRT of Ho: 0= 1, v unknown, versus H₁:01, v unknown, has critical region of the form {x: T(x) ≤ c₁ or T(x) > c₂}, where 0 < C₁ < C2 and 72 Π.Χ. i=1 T = log (min X₂)n

A random sample, X₁,..., Xn, is drawn from a Pareto population with pdf ого f(x0, v) = 20+1₁) (1), 0>0, v> 0. (a) Find the MLEs of 0 and v. (b) Show that the LRT of Ho: 0= 1, v unknown, versus H₁:01, v unknown, has critical region of the form {x: T(x) ≤ c₁ or T(x) > c₂}, where 0 < C₁ < C2 and 72 Π.Χ. i=1 T = log (min X₂)n

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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A random sample, X₁,..., Xn, is drawn from a Pareto population with pdf f(x0, v) = ого x+1v₁∞) (1), > 0, v> 0. (a) Find the MLEs of 0 and v. (b) Show that the LRT of Ho: 0= 1, v unknown, versus H₁:01, v unknown, has critical region of the form {x: T(x) ≤ c₁ or T(x) > c₂}, where 0 < C₁ < C2 and 72 Π.Χ. i=1 T = log (min X₁)n
Transcribed Image Text:A random sample, X₁,..., Xn, is drawn from a Pareto population with pdf f(x0, v) = ого x+1v₁∞) (1), > 0, v> 0. (a) Find the MLEs of 0 and v. (b) Show that the LRT of Ho: 0= 1, v unknown, versus H₁:01, v unknown, has critical region of the form {x: T(x) ≤ c₁ or T(x) > c₂}, where 0 < C₁ < C2 and 72 Π.Χ. i=1 T = log (min X₁)n
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