Chi#

class pymc_extras.distributions.Chi(name, nu, **kwargs)[source]#

\(\chi\) log-likelihood.

The pdf of this distribution is

\[f(x \mid \nu) = \frac{x^{\nu - 1}e^{-x^2/2}}{2^{\nu/2 - 1}\Gamma(\nu/2)}\]

(Source code)

Support

\(x \in [0, \infty)\)

Mean

\(\sqrt{2}\frac{\Gamma((\nu + 1)/2)}{\Gamma(\nu/2)}\)

Variance

\(\nu - 2\left(\frac{\Gamma((\nu + 1)/2)}{\Gamma(\nu/2)}\right)^2\)
Parameters:

nu (tensor_like of float) – Degrees of freedom (nu > 0).

Examples

import pymc as pm
from pymc_extras.distributions import Chi

with pm.Model():
    x = Chi("x", nu=1)
__init__()#

Methods

__init__()

chi_dist(nu, size)

dist(nu, **kwargs)