paretoCdf

Evaluates the Pareto cumulative probability distribution function.

Synopsis

paretoCdf (x, xm, k)

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 paretoCdf function evaluates the distribution function, F, of a Pareto random variable with scale parameter \(x_m\) and shape parameter k. It is given by:

\[F(x|x_m,k) = 1 - \left(\frac{x_m}{x}\right)^k\]

where \(x_m>0\) and \(k>0\). The function is only defined for \(x\geq x_m\).

Example

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

from __future__ import print_function
from numpy import *
from pyimsl.stat.paretoCdf import paretoCdf

x = 0.5
xm = 0.4
k = 0.7
pr = paretoCdf(x, xm, k)
print("Pr(x <= %3.1f) = %6.4f" % (x, pr))

Output

Pr(x <= 0.5) = 0.1446