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
\[\begin{split}f(x \mid \psi, \mu, \alpha) = \left\{ \begin{array}{l} (1-\psi) + \psi \left ( \frac{\alpha}{\alpha+\mu} \right) ^\alpha, \text{if } x = 0 \\ \psi \frac{\Gamma(x+\alpha)}{x! \Gamma(\alpha)} \left ( \frac{\alpha}{\mu+\alpha} \right)^\alpha \left( \frac{\mu}{\mu+\alpha} \right)^x, \text{if } x=1,2,3,\ldots \end{array} \right.\end{split}\](Source code, png, hires.png, pdf)
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: float
Expected proportion of NegativeBinomial variates (0 < psi < 1)
- mu: float
Poission distribution parameter (mu > 0).
- alpha: float
Gamma distribution parameter (alpha > 0).
- p: float
Alternative probability of success in each trial (0 < p < 1).
- n: float
Alternative number of target success trials (n > 0)
Methods
ZeroInflatedNegativeBinomial.__init__
(*args, ...)ZeroInflatedNegativeBinomial.dist
(psi[, mu, ...])