# BetaNegativeBinomial#

class pymc_experimental.distributions.BetaNegativeBinomial(name, alpha, beta, r, **kwargs)[source]#

Beta Negative Binomial distribution.

The pmf of this distribution is

$f(x \mid \alpha, \beta, r) = \frac{B(r + x, \alpha + \beta)}{B(r, \alpha)} \frac{\Gamma(x + \beta)}{x! \Gamma(\beta)}$

where $$B$$ is the Beta function and $$\Gamma$$ is the Gamma function.

 Support $$x \in \mathbb{N}_0$$ Mean $${\begin{cases}{\frac {r\beta }{\alpha -1}}&{\text{if}}\ \alpha >1\\\infty &{\text{otherwise}}\ \end{cases}}$$ Variance $${\displaystyle {\begin{cases}{\frac {r\beta (r+\alpha -1)(\beta +\alpha -1)}{(\alpha -2){(\alpha -1)}^{2}}}&{\text{if}}\ \alpha >2\\\infty &{\text{otherwise}}\ \end{cases}}}$$
Parameters:
• alpha (tensor_like of float) – shape of the beta distribution (alpha > 0).

• beta (tensor_like of float) – shape of the beta distribution (beta > 0).

• r (tensor_like of float) – number of successes until the experiment is stopped (integer but can be extended to real)

__init__()#

Methods

 beta_negative_binomial_dist(alpha, beta, r, size) beta_negative_binomial_logp(value, alpha, ...) dist(alpha, beta, r, **kwargs)