pymc.Gumbel#

class pymc.Gumbel(name, *args, rng=None, dims=None, initval=None, observed=None, total_size=None, transform=UNSET, **kwargs)[source]#

Univariate Gumbel log-likelihood.

The pdf of this distribution is

\[f(x \mid \mu, \beta) = \frac{1}{\beta}e^{-(z + e^{-z})}\]

where

\[z = \frac{x - \mu}{\beta}.\]

(Source code, png, hires.png, pdf)

../../../_images/pymc-Gumbel-1.png

Support

\(x \in \mathbb{R}\)

Mean

\(\mu + \beta\gamma\), where \(\gamma\) is the Euler-Mascheroni constant

Variance

\(\frac{\pi^2}{6} \beta^2\)

Parameters
mutensor_like of float

Location parameter.

betatensor_like of float

Scale parameter (beta > 0).

Methods

Gumbel.__init__(*args, **kwargs)

Gumbel.dist([mu, beta, no_assert])

Creates a tensor variable corresponding to the cls distribution.

Gumbel.logcdf(mu, beta)

Compute the log of the cumulative distribution function for Gumbel distribution at the specified value.

Gumbel.moment(size, mu, beta)

Attributes

rv_class

rv_op