3.5.3.1.24 Prob

Definition:

The prob(x) function is the Probability Density (for a normal distribution) integrated from \(-x\) to \(+x\).

It has the limiting values \(prob(0)=0\), and \(prob(\infty )=1\). Mathematically:
\(Prob(x)=\frac 1{\sqrt{2\pi }}\int_{-x}^{+x}e^{\frac{-t^2}2}dt\)

Note that \(prob(-x) = -prob(x)\), \(prob(x)= erf(\frac x{\sqrt{2}})\) or \(prob(x) = 2 * Normal Distribution Function -1\).

See Also:

erf