pymc.DiscreteWeibull#

class pymc.DiscreteWeibull(name, *args, **kwargs)[source]#

Discrete Weibull log-likelihood.

The discrete Weibull distribution is a flexible model of count data that can handle both over- and under-dispersion. The pmf of this distribution is

\[f(x \mid q, \beta) = q^{x^{\beta}} - q^{(x + 1)^{\beta}}\]

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

../../../_images/pymc-DiscreteWeibull-1.png

Support

\(x \in \mathbb{N}_0\)

Mean

\(\mu = \sum_{x = 1}^{\infty} q^{x^{\beta}}\)

Variance

\(2 \sum_{x = 1}^{\infty} x q^{x^{\beta}} - \mu - \mu^2\)

Parameters:
qtensor_like of float

Shape parameter (0 < q < 1).

betatensor_like of float

Shape parameter (beta > 0).

Methods

DiscreteWeibull.dist(q, beta, *args, **kwargs)

Creates a tensor variable corresponding to the cls distribution.