Evaluates the inverse of the standard normal (Gaussian) distribution function.

Synopsis

#include <imsls.h>

float imsls_f_normal_inverse_cdf (float p)

The type double function is imsls_d_normal_inverse_cdf.

Required Arguments

float p   (Input)
Probability for which the inverse of the normal distribution function is to be evaluated. Argument p must be in the open interval (0.0, 1.0).

Return Value

The inverse of the normal distribution function evaluated at p. The probability that a standard normal random variable takes a value less than or equal to imsls_f_normal_inverse_cdf is p.

Description

Function imsls_f_normal_inverse_cdf evaluates the inverse of the distribution function, Φ, of a standard normal (Gaussian) random variable, imsls_f_normal_inverse_cdf(p) = Φ−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 0 and a variance of 1.

Function imsls_f_normal_inverse_cdf (p) 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 imsls_f_normal_inverse_cdf are described by Kinnucan and Kuki (1968).

Example

This example computes the point such that the probability is 0.9 that a standard normal random variable is less than or equal to this point.

#include <imsls.h>

main()
{
    float       x;
    float       p = 0.9;

    x = imsls_f_normal_inverse_cdf(p);
    printf("The 90th percentile of a standard normal is %6.4f.\n", x);
}

Output

The 90th percentile of a standard normal is 1.2816.

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