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.