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IMSL_NORMALCDF

# IMSL_NORMALCDF

The IMSL_NORMALCDF function evaluates the standard normal (Gaussian) distribution function. Using a keyword, the inverse of the standard normal (Gaussian) distribution can be evaluated.

The IMSL_NORMALCDF function evaluates the distribution function, Î¦, of a standard normal (Gaussian) random variable; that is:

The value of the distribution function at the point x is the probability that the random variable takes a value less than or equal to x.

The standard normal distribution (for which IMSL_NORMALCDF is the distribution function) has mean of zero and variance of 1. The probability that a normal random variable with mean Âµ and variance Ï2 is less than y is given by IMSL_NORMALCDF evaluated at (y â Âµ)/Ï.

The function Î¦(x) is evaluated by use of the complementary error function, IMSL_ERFC. The relationship follows below:

If the keyword INVERSE is specified, the IMSL_NORMALCDF function evaluates the inverse of the distribution function, Î¦, of a standard normal (Gaussian) random variable; that is:

IMSL_NORMALCDF (x, /INVERSE) = Î¦â1 (x)

where:

The value of the distribution function at the point x is the probability that the random variable takes a value less than or equal to x. The standard normal distribution has a mean of zero and a variance of 1.

The IMSL_NORMALCDF function is evaluated by use of minimax rational-function approximations for the inverse of the error function. General descriptions of these approximations are given in Hart et al. (1968) and Strecok (1968). The rational functions used in IMSL_NORMALCDF are described by Kinnucan and Kuki (1968).

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