# dbnb: Probability density function of the BNB distribution In fipp: Induced Priors in Bayesian Mixture Models

## Description

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

## Usage

 `1` ```dbnb(x, mu, a, b, log = FALSE) ```

## Arguments

 `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).

## Details

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.

## Value

Numeric vector of density values.

## References

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

## Examples

 ``` 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 ```

fipp documentation built on Feb. 11, 2021, 5:07 p.m.