# Example of Fisher’s F distribution¶

Figure 3.16.

This shows an example of Fisher’s F distribution with various parameters. We’ll generate the distribution using:

```dist = scipy.stats.f(...)
```

Where … should be filled in with the desired distribution parameters Once we have defined the distribution parameters in this way, these distribution objects have many useful methods; for example:

• `dist.pmf(x)` computes the Probability Mass Function at values `x` in the case of discrete distributions

• `dist.pdf(x)` computes the Probability Density Function at values `x` in the case of continuous distributions

• `dist.rvs(N)` computes `N` random variables distributed according to the given distribution

Many further options exist; refer to the documentation of `scipy.stats` for more details.

```
```
```# Author: Jake VanderPlas
#   The figure produced by this code is published in the textbook
#   "Statistics, Data Mining, and Machine Learning in Astronomy" (2013)
#   To report a bug or issue, use the following forum:
import numpy as np
from scipy.stats import f as fisher_f
from matplotlib import pyplot as plt

#----------------------------------------------------------------------
# This function adjusts matplotlib settings for a uniform feel in the textbook.
# Note that with usetex=True, fonts are rendered with LaTeX.  This may
# result in an error if LaTeX is not installed on your system.  In that case,
# you can set usetex to False.
if "setup_text_plots" not in globals():
from astroML.plotting import setup_text_plots
setup_text_plots(fontsize=8, usetex=True)

#------------------------------------------------------------
# Define the distribution parameters to be plotted
mu = 0
d1_values = [1, 5, 2, 10]
d2_values = [1, 2, 5, 50]
linestyles = ['-', '--', ':', '-.']
x = np.linspace(0, 5, 1001)[1:]

fig, ax = plt.subplots(figsize=(5, 3.75))

for (d1, d2, ls) in zip(d1_values, d2_values, linestyles):
dist = fisher_f(d1, d2, mu)

plt.plot(x, dist.pdf(x), ls=ls, c='black',
label=r'\$d_1=%i,\ d_2=%i\$' % (d1, d2))

plt.xlim(0, 4)
plt.ylim(0.0, 1.0)

plt.xlabel('\$x\$')
plt.ylabel(r'\$p(x|d_1, d_2)\$')
plt.title("Fisher's Distribution")

plt.legend()
plt.show()
```