The cumulative distribution function (CDF) of the standard normal distribution, also known as the normal CDF or Φ(x), computes the probability that a standard normal random variable takes a value less than or equal to x:
\[\Phi(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{x} e^{-t^2/2} dt\]
This function is fundamental in statistics, probability theory, and quantitative finance for computing probabilities, confidence intervals, and option pricing.
Relationship to Error Function:
The normal CDF is related to the error function by:
\[\Phi(x) = \frac{1}{2} \left[ 1 + \text{erf}\left(\frac{x}{\sqrt{2}}\right) \right]\]
Note
Currently, only double-precision variants of cdfnorm are available. Single-precision variants (cdfnormf) may be added in future releases.