# 3.5.3.1.5 Cumul_normal

## Definition:

$P = cumul\_normal(x)$ evaluates the cumulative Normal distribution function

$P(x)=\frac 1{\sqrt{2\pi }}\int_{-\infty }^xe^{\frac{-u^2}2}du$

The function is based on the fact that

$P(x)=\frac 12 erfc(\frac{-x}{\sqrt{2}})$

For more information please review the s15abc function in the NAG document.

## Parameters:

x (input, double)
The argument x of the function.
$p$ (output, double)
The value of cumulative Normal distribution function