The function `ZAP`

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

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

. The functions `dZAP`

, `pZAP`

, `qZAP`

and `rZAP`

define the
density, distribution function, quantile function
and random generation for the inflated poisson, `ZAP()`

, distribution.

```
ZAP(mu.link = "log", sigma.link = "logit")
dZAP(x, mu = 5, sigma = 0.1, log = FALSE)
pZAP(q, mu = 5, sigma = 0.1, lower.tail = TRUE, log.p = FALSE)
qZAP(p, mu = 5, sigma = 0.1, lower.tail = TRUE, log.p = FALSE)
rZAP(n, mu = 5, sigma = 0.1)
```

The function `ZAP`

returns a `gamlss.family`

object which can be used to fit a zero inflated poisson distribution in the `gamlss()`

function.

- mu.link
defines the

`mu.link`

, with "log" link as the default for the`mu`

parameter- sigma.link
defines the

`sigma.link`

, with "logit" link as the default for the sigma parameter which in this case is the probability at zero. Other links are "probit" and "cloglog"'(complementary log-log)- x
vector of (non-negative integer)

- mu
vector of positive means

- sigma
vector of probabilities at zero

- 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]

Mikis Stasinopoulos, Bob Rigby

Details about the zero adjusted Poison, `ZAP`

can be found pp 494-496 of Rigby *et al.* (2019).

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, tools:::Rd_expr_doi("10.1201/9780429298547"). An older version can be found in https://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, tools:::Rd_expr_doi("10.18637/jss.v023.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. tools:::Rd_expr_doi("10.1201/b21973")

(see also https://www.gamlss.com/)..

`gamlss.family`

, `PO`

, `ZIP`

, `ZIP2`

, `ZALG`

```
ZAP()
# creating data and plotting them
dat<-rZAP(1000, mu=5, sigma=.1)
r <- barplot(table(dat), col='lightblue')
```

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