Zero-inflated inverse Gaussian distribution

Density, distribution function, and random generation for the zero-inflated inverse Gaussian distribution.

Usage

dziinvgauss(x, mean = 1, shape = 1, zeroprob = 0, log = FALSE)

pziinvgauss(q, mean = 1, shape = 1, zeroprob = 0, lower.tail = TRUE, log.p = FALSE)

rziinvgauss(n, mean = 1, shape = 1, zeroprob = 0)

Arguments

x, q

vector of quantiles

mean

location parameter

shape

shape parameter, must be positive.

zeroprob

zero-probability, must be in \([0, 1]\).

log, log.p

logical; if TRUE, probabilities/ densities \(p\) are returned as \(\log(p)\).

lower.tail

logical; if TRUE, probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).

n

number of random values to return

Value

dziinvgauss gives the density, pziinvgauss gives the distribution function, and rziinvgauss generates random deviates.

Details

This implementation of zidinvgauss allows for automatic differentiation with RTMB.

$$f(x;\,\mu,\lambda,p_0) = p_0\,\mathbf{1}[x=0] + (1-p_0)\,f_{\mathrm{IG}}(x;\,\mu,\lambda)\,\mathbf{1}[x>0],$$ where \(p_0\) is zeroprob and \(f_{\mathrm{IG}}\) is the inverse Gaussian density.

Because the continuous part places no mass at zero, zeroprob is exactly \(P(X = 0)\), and zero-inflation coincides with a hurdle model here. The two constructions only differ for discrete distributions, where the base distribution can generate zeros of its own. GAMLSS therefore calls distributions of this type zero-adjusted rather than zero-inflated, as in its ZAIG family.

Examples

x <- rziinvgauss(1, 1, 2, 0.5)
d <- dziinvgauss(x, 1, 2, 0.5)
p <- pziinvgauss(x, 1, 2, 0.5)