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 hansherman February 6th, 2014 05:25 AM

Max Transformation of a normal distributed random variable

Dear Focrum,

I have the following question that i have not been able to work out. It is out of pure interest.

Given a normal distributed random variable with:

$\rho \sim N(\bar{\rho},\sigma_{\rho}^2)$

What is then the distribution of the max-transformed random variable

$\epsilon= \max(\rho,c)$

where $c$ is some constant.