lognormal_cdf

Evaluates the lognormal cumulative distribution function (CDF).

Synopsis

#include<imsls.h>

floatimsls_f_lognormal_cdf(float x, float amu, float sigma)

The type double function is imsls_d_lognormal_cdf.

Required Arguments

floatx (Input)
Argument for which the lognormal CDF is to be evaluated. x must be non-negative.

floatamu (Input)
Location parameter of the lognormal CDF.

floatsigma (Input)
Shape parameter of the lognormal CDF.  sigma must be positive.

Return Value

The probability that a lognormal random variable takes a value less than or equal to x. A value of NaN is returned if an input value is in error.

Description

The function imsls_f_lognormal_cdf evaluates the lognormal cumulative distribution function (CDF), defined as

 

where

 

is the standard normal CDF.

Example

In this example, we evaluate the CDF at x = 0.7137, amu = 0.0,
sigma = 0.5.

 

#include <imsls.h>

#include <stdio.h>

 

int main()

{

float x = 0.7137;

float amu = 0.0;

float sigma = 0.5;

float p;

 

p = imsls_f_lognormal_cdf(x,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 %6.4f\n\n", x, p);

}

Output

The probability that lognormal random varisable X

with location parameter amu = 0.0 and shape parameter

sigma = 0.5 is less than or equal to 0.7137 is 0.2500