Description Usage Arguments Details Value References Examples

Evaluates the probability density function of the beta-negative-binomial (BNB) distribution with a mean parameter and two shape parameters.

1 |

`x` |
vector of quantiles. |

`mu` |
mean parameter. |

`a` |
1st shape parameter. |

`b` |
2nd shape parameter. |

`log` |
logical; if TRUE, density values p are given as log(p). |

The BNB distribution has density

*
f(x) = (Γ(μ + x) B(μ + a, x + b)) / (Gamma(μ) Gamma(x + 1) B(a, b)),
*

where *μ* is the mean parameter and *a* and *b* are the first and
second shape parameter.

Numeric vector of density values.

Frühwirth-Schnatter, S., Malsiner-Walli, G., and Grün, B. (2020) Generalized mixtures of finite mixtures and telescoping sampling https://arxiv.org/abs/2005.09918

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ```
## Similar to other d+DISTRIBUTION_NAME functions such as dnorm, it
## evaluates the density of a distribution (in this case the BNB distri)
## at point x
##
## Let's try with the density of x = 1 for BNB(1,4,3)
x <- 1
dbnb(x, mu = 1, a = 4, b = 3)
## The primary use of this function is in the closures returned from
## fipp() or nCluststers() as a prior on K-1
pmf <- nClusters(Kplus = 1:15, N = 100, type = "static",
gamma = 1, maxK = 150)
## Now evaluate above when K-1 ~ BNB(1,4,3)
pmf(priorK = dbnb, priorKparams = list(mu = 1, a = 4, b = 3))
## Compare the result with the case when K-1 ~ Pois(1)
pmf(priorK = dpois, priorKparams = list(lambda = 1))
## Although both BNB(1,4,3) and Pois(1) have 1 as their mean, the former
## has a fatter rhs tail. We see that it is reflected in the induced prior
## on K+ as well
``` |

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