pareto_cdf

Evaluates the Pareto cumulative probability distribution function.

Synopsis

#include <imsls.h>

float imsls_f_pareto_cdf (float x, float xm, float k)

The type double function is imsls_d_pareto_cdf.

Required Arguments

float x (Input)
Argument for which the Pareto distribution function is to be evaluated.

float xm (Input)
The scale parameter.

float k (Input)
The shape parameter.

Return Value

The probability that a Pareto random variable takes a value less than or equal to x. NaN is returned on error.

Description

The imsls_f_pareto_cdf function evaluates the distribution function, F, of a Pareto random variable with scale parameter xmand shape parameter k. It is given by:

 

where xm > 0 and k > 0. The function is only defined for x ≥ xm.

Example

Suppose X is a Pareto random variable with xm = 0.4 and k = 0.7. The function finds the probability that X is less than or equal to 0.5.

 

#include <imsls.h>

#include <stdio.h>

 

int main(){

float x = 0.5;

float xm = 0.4;

float k = 0.7;

float pr = 0.0;

 

pr = imsls_f_pareto_cdf(x, xm, k);

printf("Pr(x <= %3.1f) = %6.4f\n", x, pr);

}

Output

 

Pr(x <= 0.5) = 0.1446