unit normal loss function

The function, $UNL$, is defined by

$$UNL(c)={\int }_c^{\mathrm{\infty }}(t-c)f(t)𝑑t$$

where $c$ is a constant and $f(.)$ is the normal probability distribution function.
An alternative computational formula for $UNL$ is the following:

$$UNL(z)=f(z)-z(1-F(z))$$

where $f(.)$ and $F(.)$ are the probability distribution function and cumulative distribution function for Standard Normal Distribution respectively.
Remark. This function has an extensive use in Risk Analysis and the Theory of Blackjack.

Title	unit normal loss function
Canonical name	UnitNormalLossFunction
Date of creation	2013-03-22 15:56:42
Last modified on	2013-03-22 15:56:42
Owner	georgiosl (7242)
Last modified by	georgiosl (7242)
Numerical id	6
Author	georgiosl (7242)
Entry type	Definition
Classification	msc 62E15