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Show that Y = log(X) ~ Exp(0), i.e., the log of a Pareto distribution is simply an exponential distribution with scale 0. Hint

Show that Y = log(X) ~ Exp(0), i.e., the log of a Pareto distribution is simply an exponential distribution with scale 0. Hint

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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Let X~ Pareto (0) be a random variable with the Pareto distribution, whose pdf is given by = {1+-+*) [¼x−(¹+1), x>1 x <i fx(x; 0) =
Transcribed Image Text:Let X~ Pareto (0) be a random variable with the Pareto distribution, whose pdf is given by = {1+-+*) [¼x−(¹+1), x>1 x <i fx(x; 0) =
1. Show that Y = log(X) ~ Exp(0), i.e., the log of a Pareto distribution is simply an exponential distribution with scale 0. Hint Use the change of variables formula, i.e., if Y = g(X) then d 1 7 9 1 (0)| dy fy(y;0) = fx (9¯¹(y); 0)) · ·|
Transcribed Image Text:1. Show that Y = log(X) ~ Exp(0), i.e., the log of a Pareto distribution is simply an exponential distribution with scale 0. Hint Use the change of variables formula, i.e., if Y = g(X) then d 1 7 9 1 (0)| dy fy(y;0) = fx (9¯¹(y); 0)) · ·|
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