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

scipy.stats.dgamma = <scipy.stats._continuous_distns.dgamma_gen object>[source]#

A double gamma continuous random variable.

The double gamma distribution is also known as the reflected gamma distribution [1].

As an instance of the rv_continuous class, dgamma 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 dgamma is:

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

for a real number \(x\) and \(a > 0\). \(\Gamma\) is the gamma function (scipy.special.gamma).

dgamma takes a as a shape parameter for \(a\).

The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the loc and scale parameters. Specifically, dgamma.pdf(x, a, loc, scale) is identically equivalent to dgamma.pdf(y, a) / 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

[1]

Johnson, Kotz, and Balakrishnan, “Continuous Univariate Distributions, Volume 1”, Second Edition, John Wiley and Sons (1994).

Examples

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

Calculate the first four moments:

a = 1.1 mean, var, skew, kurt = dgamma.stats(a, moments='mvsk')

Display the probability density function (pdf):

x = np.linspace(dgamma.ppf(0.01, a), ... dgamma.ppf(0.99, a), 100) ax.plot(x, dgamma.pdf(x, a), ... 'r-', lw=5, alpha=0.6, label='dgamma 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 = dgamma(a) ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

Check accuracy of cdf and ppf:

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

Generate random numbers:

r = dgamma.rvs(a, 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