pymc.ZeroInflatedNegativeBinomial#

class pymc.ZeroInflatedNegativeBinomial(name, psi, mu=None, alpha=None, p=None, n=None, **kwargs)[source]#

Zero-Inflated Negative binomial log-likelihood.

The Zero-inflated version of the Negative Binomial (NB). The NB distribution describes a Poisson random variable whose rate parameter is gamma distributed. The pmf of this distribution is

$\begin{split}f(x \mid \psi, \mu, \alpha) = \left\{ \begin{array}{l} (1-\psi) + \psi \left ( \frac{\alpha}{\alpha+\mu} \right) ^\alpha, \text{if } x = 0 \\ \psi \frac{\Gamma(x+\alpha)}{x! \Gamma(\alpha)} \left ( \frac{\alpha}{\mu+\alpha} \right)^\alpha \left( \frac{\mu}{\mu+\alpha} \right)^x, \text{if } x=1,2,3,\ldots \end{array} \right.\end{split}$
 Support $$x \in \mathbb{N}_0$$ Mean $$\psi\mu$$ Var $$\psi\mu + \left (1 + \frac{\mu}{\alpha} + \frac{1-\psi}{\mu} \right)$$

The zero inflated negative binomial distribution can be parametrized either in terms of mu or p, and either in terms of alpha or n. The link between the parametrizations is given by

$\begin{split}\mu &= \frac{n(1-p)}{p} \\ \alpha &= n\end{split}$
Parameters
psi

Expected proportion of NegativeBinomial variates (0 < psi < 1)

mu

Poission distribution parameter (mu > 0).

alpha

Gamma distribution parameter (alpha > 0).

p

Alternative probability of success in each trial (0 < p < 1).

n

Alternative number of target success trials (n > 0)

Methods

 ZeroInflatedNegativeBinomial.__init__(*args, ...) ZeroInflatedNegativeBinomial.dist(psi[, mu, ...])