pareto_pdf

Evaluates the Pareto probability density function.

Synopsis

#include <imsls.h>

float imsls_f_pareto_pdf (float x, float xm, float k)

The type double function is imsls_d_pareto_pdf.

Required Arguments

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

float xm (Input)
The scale parameter.

float k (Input)
The shape parameter.

Return Value

The probability density at x. NaN is returned on error.

Description

The probability density function of the Pareto distribution is:

 

where the scale parameter xm > 0 and the shape parameter k > 0. The function is only defined for x ≥ xm.

Example

In this example, we evaluate the Pareto PDF at x = 0.5, xm = 0.4 and k = 0.7.

 

#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_pdf(x, xm, k);

printf("The probability density of a Pareto random");

printf("variable X with\na scale parameter xm = ");

printf("%3.1f and a shape parameter ", xm);

printf("k = %3.1f\nand value x = %3.1f is %6.4f.\n",

k, x, pr);

}

Output

 

The probability density of a Pareto random variable X with

a scale parameter xm = 0.4 and a shape parameter k = 0.7

and value x = 0.5 is 1.1975.