bundles / scipy latest / scipy / stats / _continuous_distns / levy_gen

class

`scipy.stats._continuous_distns:levy_gen`

source: build-install/usr/lib/python3.14/site-packages/scipy/stats/_continuous_distns.py:6313

Signature

class levy_gen(momtype = 1, a = None, b = None, xtol = 1e-14, badvalue = None, name = None, longname = None, shapes = None, seed = None)

Members

Summary

A Levy continuous random variable.

Extended Summary

%(before_notes)s

Notes

The probability density function for levy is:

f (x) = \frac{1}{2 π x ^{3}} exp (- \frac{1}{2 x})

for $x > 0$ .

This is the same as the Levy-stable distribution with $a = 1/2$ and $b = 1$ .

%(after_notes)s

Examples

import numpy as np
from scipy.stats import levy
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)

✓

Calculate the first four moments:

mean, var, skew, kurt = levy.stats(moments='mvsk')

✓

Display the probability density function (``pdf``):

a, b = levy.ppf(0), levy.ppf(0.6)
x = np.linspace(a, b, 100)

✓

ax.plot(x, levy.pdf(x),
       'r-', lw=5, alpha=0.6, label='levy pdf')

✗

[<matplotlib.lines.Line2D object at 0x7f3f601c2e40>]

Alternatively, the distribution object can be called (as a function) to fix the shape, location and scale parameters. This returns a "frozen" RV object holding the given parameters fixed. Freeze the distribution and display the frozen ``pdf``:

rv = levy()

✓

ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

✗

[<matplotlib.lines.Line2D object at 0x7f3f601c3380>]

Check accuracy of ``cdf`` and ``ppf``:

vals = levy.ppf([0.001, 0.5, 0.999])
np.allclose([0.001, 0.5, 0.999], levy.cdf(vals))

✓

True

Generate random numbers:

r = levy.rvs(size=1000)

✓

And compare the histogram:

bins = np.concatenate((np.linspace(a, b, 20), [np.max(r)]))

✓

ax.hist(r, bins=bins, density=True, histtype='stepfilled', alpha=0.2)
ax.set_xlim([x[0], x[-1]])
ax.legend(loc='best', frameon=False)

✗

<matplotlib.legend.Legend object at 0x7f3f601c1160>

plt.show()

✓

Aliases

scipy.stats._continuous_distns.levy_gen