# pymc.Gamma#

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

Gamma log-likelihood.

Represents the sum of alpha exponentially distributed random variables, each of which has rate beta.

The pdf of this distribution is

$f(x \mid \alpha, \beta) = \frac{\beta^{\alpha}x^{\alpha-1}e^{-\beta x}}{\Gamma(\alpha)}$
 Support $$x \in (0, \infty)$$ Mean $$\dfrac{\alpha}{\beta}$$ Variance $$\dfrac{\alpha}{\beta^2}$$

Gamma distribution can be parameterized either in terms of alpha and beta or mean and standard deviation. The link between the two parametrizations is given by

$\begin{split}\alpha &= \frac{\mu^2}{\sigma^2} \\ \beta &= \frac{\mu}{\sigma^2}\end{split}$
Parameters
alphatensor_like of float, optional

Shape parameter (alpha > 0).

betatensor_like of float, optional

Rate parameter (beta > 0).

mutensor_like of float, optional

Alternative shape parameter (mu > 0).

sigmatensor_like of float, optional

Alternative scale parameter (sigma > 0).

Methods

 Gamma.__init__(*args, **kwargs) Gamma.dist([alpha, beta, mu, sigma]) Creates a tensor variable corresponding to the cls distribution. Gamma.get_alpha_beta([alpha, beta, mu, sigma]) Gamma.logcdf(alpha, inv_beta) Gamma.logp(alpha, inv_beta) Gamma.moment(size, alpha, inv_beta)

Attributes

 rv_op