bundles / scipy latest / scipy / stats / _continuous_distns / vonmises_gen

class

`scipy.stats._continuous_distns:vonmises_gen`

source: /scipy/stats/_continuous_distns.py :11072

Signature

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

Members

Summary

A Von Mises continuous random variable.

Extended Summary

%(before_notes)s

Notes

The probability density function for vonmises and vonmises_line is:

f (x, κ) = \frac{exp ( κ cos ( x ))}{2 π I _{0} ( κ )}

for $- π \leq x \leq π$ , $κ \geq 0$ . $I_{0}$ is the modified Bessel function of order zero (scipy.special.i0).

vonmises is a circular distribution which does not restrict the distribution to a fixed interval. Currently, there is no circular distribution framework in SciPy. The cdf is implemented such that cdf(x + 2*np.pi) == cdf(x) + 1.

vonmises_line is the same distribution, defined on $[- π, π]$ on the real line. This is a regular (i.e. non-circular) distribution.

Note about distribution parameters: vonmises and vonmises_line take kappa as a shape parameter (concentration) and loc as the location (circular mean). A scale parameter is accepted but does not have any effect.

Examples

Import the necessary modules.

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

✓

Define distribution parameters.

loc = 0.5 * np.pi  # circular mean
kappa = 1  # concentration

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Compute the probability density at ``x=0`` via the ``pdf`` method.

vonmises.pdf(0, loc=loc, kappa=kappa)

✗

Verify that the percentile function ``ppf`` inverts the cumulative distribution function ``cdf`` up to floating point accuracy.

x = 1
cdf_value = vonmises.cdf(x, loc=loc, kappa=kappa)
ppf_value = vonmises.ppf(cdf_value, loc=loc, kappa=kappa)

✓

x, cdf_value, ppf_value

✗

Draw 1000 random variates by calling the ``rvs`` method.

sample_size = 1000
sample = vonmises(loc=loc, kappa=kappa).rvs(sample_size)

✓

Plot the von Mises density on a Cartesian and polar grid to emphasize that it is a circular distribution.

fig = plt.figure(figsize=(12, 6))
left = plt.subplot(121)
right = plt.subplot(122, projection='polar')
x = np.linspace(-np.pi, np.pi, 500)
vonmises_pdf = vonmises.pdf(x, loc=loc, kappa=kappa)
ticks = [0, 0.15, 0.3]

✓

The left image contains the Cartesian plot.

left.plot(x, vonmises_pdf)
left.set_yticks(ticks)

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number_of_bins = int(np.sqrt(sample_size))

✓

left.hist(sample, density=True, bins=number_of_bins)
left.set_title("Cartesian plot")
left.set_xlim(-np.pi, np.pi)

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left.grid(True)

✓

The right image contains the polar plot.

right.plot(x, vonmises_pdf, label="PDF")
right.set_yticks(ticks)
right.hist(sample, density=True, bins=number_of_bins,
           label="Histogram")
right.set_title("Polar plot")
right.legend(bbox_to_anchor=(0.15, 1.06))

✗

Aliases

scipy.stats._continuous_distns.vonmises_gen