# Zero inflated and zero adjusted Binomial distribution for fitting in GAMLSS

### Description

The function `ZIBB`

defines the zero inflated beta binomial distribution, a three parameter distribution,
for a `gamlss.family`

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

.
The functions `dZIBB`

, `pZIBB`

, `qZIBB`

and `rZINN`

define the
density, distribution function, quantile function
and random generation for the zero inflated beta binomial, `ZIBB`

, distribution.

The function `ZABB`

defines the zero adjusted beta binomial distribution, a three parameter distribution, for a
`gamlss.family`

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

. The functions `dZABB`

, `pZABB`

,
`qZABB`

and `rZABB`

define the
density, distribution function, quantile function
and random generation for the zero inflated beta binomial, `ZABB()`

, distribution.

### Usage

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
ZABB(mu.link = "logit", sigma.link = "log", nu.link = "logit")
ZIBB(mu.link = "logit", sigma.link = "log", nu.link = "logit")
dZIBB(x, mu = 0.5, sigma = 0.5, nu = 0.1, bd = 1, log = FALSE)
dZABB(x, mu = 0.5, sigma = 0.1, nu = 0.1, bd = 1, log = FALSE)
pZIBB(q, mu = 0.5, sigma = 0.5, nu = 0.1, bd = 1, lower.tail = TRUE, log.p = FALSE)
pZABB(q, mu = 0.5, sigma = 0.1, nu = 0.1, bd = 1, lower.tail = TRUE, log.p = FALSE)
qZIBB(p, mu = 0.5, sigma = 0.5, nu = 0.1, bd = 1, lower.tail = TRUE, log.p = FALSE)
qZABB(p, mu = 0.5, sigma = 0.1, nu = 0.1, bd = 1, lower.tail = TRUE, log.p = FALSE)
rZIBB(n, mu = 0.5, sigma = 0.5, nu = 0.1, bd = 1)
rZABB(n, mu = 0.5, sigma = 0.1, nu = 0.1, bd = 1)
``` |

### Arguments

`mu.link` |
Defines the |

`sigma.link` |
Defines the |

`nu.link` |
Defines the |

`x` |
vector of (non-negative integer) quantiles |

`mu` |
vector of positive probabilities |

`sigma` |
vector of positive dispertion parameter |

`nu` |
vector of positive probabilities |

`bd` |
vector of binomial denominators |

`p` |
vector of probabilities |

`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] |

### Details

For the definition of the distributions see Rigby and Stasinopoulos (2010) below.

### Value

The functions `ZIBB`

and `ZABB`

return a `gamlss.family`

object which can be used to fit a
zero inflated or zero adjusted beta binomial distribution respectively in the `gamlss()`

function.

### Author(s)

Mikis Stasinopoulos mikis.stasinopoulos@gamlss.org, Bob Rigby

### References

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.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

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.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or see http://www.gamlss.com/)

### See Also

`gamlss.family`

, `NBI`

, `NBII`

### Examples

1 2 3 4 5 6 7 |