Companion

Computes the cumulative distribution function for a standard normal distribution using Taylor approximation.

Computes the cumulative distribution function for a standard normal distribution from Abramovitz and Stegun, see also Didier H. Besset Object-oriented Implementation of Numerical Methods, Morgan-Kaufmann (2001)

Computes the complementary cumulative probability for the standard normal distribution function for given value of z

Computes the first order loss function for the standard normal distribution function for given value of x, G1(z) = Emax(Z-z,0)

Computes the inverse cumulative distribution function for a standard normal distribution see, W. J. Cody, Rational Chebyshev approximations for the error function Math. Comp. pp 631-638 this is without the extra refinement and has relative error of 1.15e-9 http://www.math.uio.no/~jacklam/notes/invnorm/

Computes the pdf function for a standard normal distribution from Abramovitz and Stegun, see also Didier H. Besset Object-oriented Implementation of Numerical Methods, Morgan-Kaufmann (2001)

Computes the 2nd order loss function for the standard normal distribution function for given value of z, G2(z) = (1/2)Emax(Z-z,0)*max(Z-z-1,0)