`scipy.stats._continuous_distns:levy_l_gen`

source: /scipy/stats/_continuous_distns.py :6365

Signature

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

Members

Summary

A left-skewed Levy continuous random variable.

Extended Summary

%(before_notes)s

Notes

The probability density function for levy_l is:

f (x) = \frac{1}{∣ x ∣ 2 π ∣ x ∣} 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_l
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)

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Calculate the first four moments:

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

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

a, b = levy_l.ppf(0.4), levy_l.ppf(1)
x = np.linspace(a, b, 100)

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

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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_l()

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

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

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

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Generate random numbers:

r = levy_l.rvs(size=1000)

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And compare the histogram:

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

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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)

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plt.show()

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Aliases

scipy.stats._continuous_distns.levy_l_gen