[SciPy-User] Gamma Distribution

[Warren Weckesser]

On Tue, May 20, 2014 at 11:28 AM, Klausen Schaefersinho <
klaus.schaefers at gmail.com> wrote:

> Hi,
>
> I have a short questions with regards to the parametrization of the gamma
> distribution in the scipy.stats module. According to wikipedia, there are
> three common ways to parameterize the gamma distrubution:
>
>
>    1. With a shape parameter<http://en.wikipedia.org/wiki/Shape_parameter>
>    *k* and a scale parameter<http://en.wikipedia.org/wiki/Scale_parameter>θ.
>    2. With a shape parameter *α* = *k* and an inverse scale parameter
>    β = 1/θ, called a rate parameter<http://en.wikipedia.org/wiki/Rate_parameter>
>    .
>    3. With a shape parameter *k* and a mean parameter μ = *k*/β.
>
>
> Which one is used in Scipy and how do those parameters map to the a ,
> location and shape?
>
>
scipy.stats.gamma uses the first parametrization.  wikipedia's `k`
corresponds to the shape parameter `a`, and `theta` corresponds to the
scale parameter.  Like all of the distributions in scipy.stats, gamma also
has the location parameter `loc`, but it is usually not used.

This script reproduces the first plot on the wikipedia page.


import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import gamma


x = np.linspace(0, 20, 201)

params = [(1, 2, 'r'), (2, 2, 'g'), (3, 2, 'b'), (5, 1, 'c'), (9, 0.5, 'y')]
for k, scale, clr in params:
    lbl = r"k = %3.1f, $\theta$ = %3.1f" % (k, scale)
    plt.plot(x, gamma.pdf(x, k, scale=scale), clr, label=lbl)
plt.title("Probability density function")
plt.legend()

plt.show()


Warren


Best Regards,
>
> Klaus
>
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