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

scipy.stats.planck = <scipy.stats._discrete_distns.planck_gen object>[source]#

A Planck discrete exponential random variable.

As an instance of the rv_discrete class, planck 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 mass function for planck is:

\[f(k) = (1-\exp(-\lambda)) \exp(-\lambda k)\]

for \(k \ge 0\) and \(\lambda > 0\).

planck takes \(\lambda\) as shape parameter. The Planck distribution can be written as a geometric distribution (geom) with\(p = 1 - \exp(-\lambda)\) shifted by loc = -1.

The probability mass function above is defined in the “standardized” form. To shift distribution use the loc parameter. Specifically, planck.pmf(k, lambda_, loc) is identically equivalent to planck.pmf(k - loc, lambda_).

Examples

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

Calculate the first four moments:

lambda_ = 0.51 mean, var, skew, kurt = planck.stats(lambda_, moments='mvsk')

Display the probability mass function (pmf):

x = np.arange(planck.ppf(0.01, lambda_), ... planck.ppf(0.99, lambda_)) ax.plot(x, planck.pmf(x, lambda_), 'bo', ms=8, label='planck pmf') ax.vlines(x, 0, planck.pmf(x, lambda_), colors='b', lw=5, alpha=0.5)

Alternatively, the distribution object can be called (as a function) to fix the shape and location. This returns a “frozen” RV object holding the given parameters fixed.

Freeze the distribution and display the frozen pmf:

rv = planck(lambda_) ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1, ... label='frozen pmf') ax.legend(loc='best', frameon=False) plt.show()

Check accuracy of cdf and ppf:

prob = planck.cdf(x, lambda_) np.allclose(x, planck.ppf(prob, lambda_)) True

Generate random numbers:

r = planck.rvs(lambda_, size=1000)

Methods