Description Usage Arguments Details Value Warning Note Author(s) References See Also Examples

This function defines the beta binomial distribution, a two parameter distribution, for a `gamlss.family`

object to be used in a
GAMLSS fitting using the function gamlss()

1 2 3 4 5 6 7 |

`mu.link` |
Defines the |

`sigma.link` |
Defines the |

`mu` |
vector of positive probabilities |

`sigma` |
the dispersion parameter |

`bd` |
vector of binomial denominators |

`p` |
vector of probabilities |

`x,q` |
vector of quantiles |

`n` |
number of random values to return |

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

`lower.tail` |
logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x] |

`fast` |
a logical variable if |

Definition file for beta binomial distribution.

*f(y|mu,sigma)=[Gamma(n+1)/Gamma(y+1)/Gamma(n-y+1)]*[Gamma(y+mu/sigma)*Gamma(1/sigma)*Gamma[n+(1-mu)/sigma-y]]/[Gamma(n+(1/sigma)) * Gamma(mu/sigma) * Gamma((1-mu)/sigma)]*

for *y=0,1,2,…,n*, *0<μ<1* and *σ>0*. For *μ=0.5* and *σ=0.5* the distribution is uniform.

Returns a `gamlss.family`

object which can be used to fit a Beta Binomial distribution in the `gamlss()`

function.

The functions `pBB`

and `qBB`

are calculated using a laborious procedure so they are relatively slow.

The response variable should be a matrix containing two columns, the first with the count of successes and the second with the count of failures.
The parameter `mu`

represents a probability parameter with limits *0 < mu <1*.
*n*mu* is the mean of the distribution where n is the binomial denominator.
*[n mu (1-mu)[1+(n-1) sigma/(sigma+1)]\]^0.5* is the standard deviation of the
Beta Binomial distribution. Hence *sigma* is a dispersion type parameter

Mikis Stasinopoulos, Bob Rigby and Kalliope Akantziliotou

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),
*Appl. Statist.*, **54**, part 3, pp 507-554.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019)
*Distributions for modeling location, scale, and shape: Using GAMLSS in R*, Chapman and Hall/CRC. An older version can be found in http://www.gamlss.com/.

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.
*Journal of Statistical Software*, Vol. **23**, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017)
*Flexible Regression and Smoothing: Using GAMLSS in R*, Chapman and Hall/CRC.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ```
# BB()# gives information about the default links for the Beta Binomial distribution
#plot the pdf
plot(function(y) dBB(y, mu = .5, sigma = 1, bd =40), from=0, to=40, n=40+1, type="h")
#calculate the cdf and plotting it
ppBB <- pBB(seq(from=0, to=40), mu=.2 , sigma=3, bd=40)
plot(0:40,ppBB, type="h")
#calculating quantiles and plotting them
qqBB <- qBB(ppBB, mu=.2 , sigma=3, bd=40)
plot(qqBB~ ppBB)
# when the argument fast is useful
p <- pBB(c(0,1,2,3,4,5), mu=.01 , sigma=1, bd=5)
qBB(p, mu=.01 , sigma=1, bd=5, fast=TRUE)
# 0 1 1 2 3 5
qBB(p, mu=.01 , sigma=1, bd=5, fast=FALSE)
# 0 1 2 3 4 5
# generate random sample
tN <- table(Ni <- rBB(1000, mu=.2, sigma=1, bd=20))
r <- barplot(tN, col='lightblue')
# fitting a model
# library(gamlss)
#data(aep)
# fits a Beta-Binomial model
#h<-gamlss(y~ward+loglos+year, sigma.formula=~year+ward, family=BB, data=aep)
``` |

```
Loading required package: MASS
[1] 0 1 2 3 4 5
[1] 0 1 2 3 4 5
```

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.