lognormal_inverse_cdf
Evaluates the inverse of the lognormal cumulative distribution function (CDF).
Synopsis
#include<imsls.h>
floatimsls_f_lognormal_inverse_cdf(float p, float amu, float sigma)
The type double function is imsls_d_lognormal_inverse_cdf.
Required Arguments
floatp (Input)
Probability for which the inverse of the lognormal CDF is to be evaluated. p must lie in the closed interval [0, 1].
floatamu (Input)
Location parameter of the lognormal CDF.
floatsigma (Input)
Shape parameter of the lognormal CDF. sigma must be positive.
Return Value
Function value, the probability that a lognormal random variable takes a value less than or equal to the returned value is the input probability p. A value of NaN is returned if an input value is in error.
Description
The function imsls_f_lognormal_inverse_cdf evaluates the inverse CDF of a lognormal random variable with location parameter amu and scale parameter sigma. The probability that a standard lognormal random variable takes a value less than or equal to the returned value is p (p=P).
where
In other words
Example
In this example, we evaluate the inverse CDF at p = 0.25, amu = 0.0, sigma = 0.5.
#include <imsls.h>
#include <stdio.h>
int main()
{
float p = 0.25;
float amu = 0.0;
float sigma = 0.5;
float x;
x = imsls_f_lognormal_inverse_cdf(p, amu, sigma);
printf("The probability that lognormal random ");
printf("variable X\n");
printf("with location parameter amu = %3.1f ", amu);
printf("and shape parameter\nsigma = %3.1f ", sigma);
printf("is less than or equal to ");
printf("%6.4f is %4.2f\n\n", x, p);
}
Output
The probability that lognormal random variable X
with location parameter amu = 0.0 and shape parameter
sigma = 0.5 is less than or equal to 0.7137 is 0.25
