scipy.stats.boltzmann — SciPy v1.15.3 Manual (original) (raw)

scipy.stats.boltzmann = <scipy.stats._discrete_distns.boltzmann_gen object>[source]#

A Boltzmann (Truncated Discrete Exponential) random variable.

As an instance of the rv_discrete class, boltzmann 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 boltzmann is:

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

for \(k = 0,..., N-1\).

boltzmann takes \(\lambda > 0\) and \(N > 0\) as shape parameters.

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

Examples

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

Calculate the first four moments:

lambda_, N = 1.4, 19 mean, var, skew, kurt = boltzmann.stats(lambda_, N, moments='mvsk')

Display the probability mass function (pmf):

x = np.arange(boltzmann.ppf(0.01, lambda_, N), ... boltzmann.ppf(0.99, lambda_, N)) ax.plot(x, boltzmann.pmf(x, lambda_, N), 'bo', ms=8, label='boltzmann pmf') ax.vlines(x, 0, boltzmann.pmf(x, lambda_, N), 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 = boltzmann(lambda_, N) 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 = boltzmann.cdf(x, lambda_, N) np.allclose(x, boltzmann.ppf(prob, lambda_, N)) True

Generate random numbers:

r = boltzmann.rvs(lambda_, N, size=1000)

Methods