Zero inflated Poisson inverse Gaussian distributions for fitting a GAMLSS model

Description

The function ZIPIG defines the zero inflated Poisson inverse Gaussian distribution, a three parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). The functions dZIPIG, pZIPIG, qZIPIG and rZIPIG define the density, distribution function, quantile function and random generation for the zero inflated negative binomial, ZIPIG(), distribution.

Usage

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ZIPIG(mu.link = "log", sigma.link = "log", nu.link = "logit")
dZIPIG(x, mu = 1, sigma = 1, nu = 0.3, log = FALSE)
pZIPIG(q, mu = 1, sigma = 1, nu = 0.3, lower.tail = TRUE, log.p = FALSE)
qZIPIG(p, mu = 1, sigma = 1, nu = 0.3, lower.tail = TRUE, log.p = FALSE)
rZIPIG(n, mu = 1, sigma = 1, nu = 0.3)

Arguments

mu.link

Defines the mu.link, with "log" link as the default for the mu parameter

sigma.link

Defines the sigma.link, with "log" link as the default for the sigma parameter

nu.link

Defines the mu.link, with "logit" link as the default for the nu parameter

x

vector of (non-negative integer) quantiles

mu

vector of positive means

sigma

vector of positive despersion parameter

nu

vector of zero probability parameter

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 distribution see Rigby and Stasinopoulos (2010) below.

Value

The function ZIPIG return a gamlss.family object which can be used to fit a zero inflated Poisson inverse Gaussian 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.org/)

See Also

gamlss.family, PIG

Examples

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ZIPIG()
# creating data and plotting them 
 dat <- rZIPIG(1000, mu=5, sigma=.5, nu=0.1)
   r <- barplot(table(dat), col='lightblue')
 

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