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