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
