3.12 Probability-Related Functions

3.12.1 Normal Cumulative Distribution Functions

The error function erf is related to the standard normal cumulative distribution function \(\Phi\) by scaling. See section normal distribution for the general normal cumulative distribution function (and its complement).

R erf(T x)
error function, also known as the Gauss error function, of x

R erfc(T x)
complementary error function of x

R Phi(T x)
standard normal cumulative distribution function of x

R inv_Phi(T x)
standard normal inverse cumulative distribution function of p, otherwise known as the quantile function

R Phi_approx(T x)
fast approximation of the unit (may replace Phi for probit regression with maximum absolute error of 0.00014, see (Bowling et al. 2009) for details)

References

Bowling, Shannon R., Mohammad T. Khasawneh, Sittichai Kaewkuekool, and Byung Rae Cho. 2009. “A Logistic Approximation to the Cumulative Normal Distribution.” Journal of Industrial Engineering and Management 2 (1): 114–27.