The `ZABI()`

function defines the zero adjusted binomial distribution, a two parameter distribution,
for a `gamlss.family`

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

.
The functions `dZABI`

, `pZABI`

, `qZABI`

and `rZABI`

define the density, distribution function, quantile function and random
generation for the zero adjusted binomial, `ZABI()`

, distribution.

The `ZIBI()`

function defines the zero inflated binomial distribution, a two parameter distribution,
for a `gamlss.family`

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

.
The functions `dZIBI`

, `pZIBI`

, `qZIBI`

and `rZIBI`

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

, distribution.

1 2 3 4 5 6 7 8 9 10 11 | ```
ZABI(mu.link = "logit", sigma.link = "logit")
dZABI(x, bd = 1, mu = 0.5, sigma = 0.1, log = FALSE)
pZABI(q, bd = 1, mu = 0.5, sigma = 0.1, lower.tail = TRUE, log.p = FALSE)
qZABI(p, bd = 1, mu = 0.5, sigma = 0.1, lower.tail = TRUE, log.p = FALSE)
rZABI(n, bd = 1, mu = 0.5, sigma = 0.1)
ZIBI(mu.link = "logit", sigma.link = "logit")
dZIBI(x, bd = 1, mu = 0.5, sigma = 0.1, log = FALSE)
pZIBI(q, bd = 1, mu = 0.5, sigma = 0.1, lower.tail = TRUE, log.p = FALSE)
qZIBI(p, bd = 1, mu = 0.5, sigma = 0.1, lower.tail = TRUE, log.p = FALSE)
rZIBI(n, bd = 1, mu = 0.5, sigma = 0.1)
``` |

`mu.link` |
Defines the |

`sigma.link` |
Defines the |

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

`mu` |
vector of positive probabilities |

`sigma` |
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] |

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

The functions `ZABI`

and `ZIBI`

return a `gamlss.family`

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

function.

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.

Mikis Stasinopoulos, Bob Rigby

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.org/)

1 2 3 4 5 6 7 8 9 | ```
ZABI()
curve(dZABI(x, mu = .5, bd=10), from=0, to=10, n=10+1, type="h")
tN <- table(Ni <- rZABI(1000, mu=.2, sigma=.3, bd=10))
r <- barplot(tN, col='lightblue')
ZIBI()
curve(dZIBI(x, mu = .5, bd=10), from=0, to=10, n=10+1, type="h")
tN <- table(Ni <- rZIBI(1000, mu=.2, sigma=.3, bd=10))
r <- barplot(tN, col='lightblue')
``` |

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