scipy.stats.nakagami — SciPy v1.15.2 Manual (original) (raw)

scipy.stats.nakagami = <scipy.stats._continuous_distns.nakagami_gen object>[source]#

A Nakagami continuous random variable.

As an instance of the rv_continuous class, nakagami object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.

Notes

The probability density function for nakagami is:

\[f(x, \nu) = \frac{2 \nu^\nu}{\Gamma(\nu)} x^{2\nu-1} \exp(-\nu x^2)\]

for \(x >= 0\), \(\nu > 0\). The distribution was introduced in[2], see also [1] for further information.

nakagami takes nu as a shape parameter for \(\nu\).

The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the loc and scale parameters. Specifically, nakagami.pdf(x, nu, loc, scale) is identically equivalent to nakagami.pdf(y, nu) / scale withy = (x - loc) / scale. Note that shifting the location of a distribution does not make it a “noncentral” distribution; noncentral generalizations of some distributions are available in separate classes.

References

[2]

M. Nakagami, “The m-distribution - A general formula of intensity distribution of rapid fading”, Statistical methods in radio wave propagation, Pergamon Press, 1960, 3-36.DOI:10.1016/B978-0-08-009306-2.50005-4

Examples

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

Calculate the first four moments:

nu = 4.97 mean, var, skew, kurt = nakagami.stats(nu, moments='mvsk')

Display the probability density function (pdf):

x = np.linspace(nakagami.ppf(0.01, nu), ... nakagami.ppf(0.99, nu), 100) ax.plot(x, nakagami.pdf(x, nu), ... 'r-', lw=5, alpha=0.6, label='nakagami pdf')

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

Check accuracy of cdf and ppf:

vals = nakagami.ppf([0.001, 0.5, 0.999], nu) np.allclose([0.001, 0.5, 0.999], nakagami.cdf(vals, nu)) True

Generate random numbers:

r = nakagami.rvs(nu, size=1000)

And compare the histogram:

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

Methods