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