exponentialPdf¶

Evaluates the exponential probability density function (PDF).

Synopsis¶

exponentialPdf (x, b)

Required Arguments¶

float x (Input): Argument for which the exponential PDF is to be evaluated. x must be non-negative.
float b (Input): Scale parameter of the exponential PDF. b must be positive.

Return Value¶

The value of the exponential probability density function with argument x and scale parameter b. A value of NaN is returned if an input value is in error.

Description¶

The function exponentialPdf evaluates the exponential probability density function. The exponential distribution is a special case of the gamma distribution and is defined as

\[f(x|b) = \mathit{\Gamma}(x|1,b) = \frac{1}{b} e^{-\tfrac{x}{b}}\]

Example¶

In this example, we evaluate the exponential PDF at x = 2.0, b = 1.0.

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

x = 2.0
b = 1.0

p = exponentialPdf(x, b)
print("The probability density of exponential random variable X")
print("with scale parameter b = %3.1f and value x = %3.1f is %6.4f" %
      (b, x, p))

Output¶

The probability density of exponential random variable X
with scale parameter b = 1.0 and value x = 2.0 is 0.1353