gamlss.dist (version 6.1-1)

ZAP: Zero adjusted poisson distribution for fitting a GAMLSS model

Description

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.

Usage

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)

Value

The function ZAP returns a gamlss.family object which can be used to fit a zero inflated poisson distribution in the gamlss() function.

Arguments

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]

Author

Mikis Stasinopoulos, Bob Rigby

Details

Details about the zero adjusted Poison, ZAP can be found pp 494-496 of Rigby et al. (2019).

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.

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/)..

See Also

gamlss.family, PO, ZIP, ZIP2, ZALG

Examples

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