Zero-inflated Weibull distribution — ziweibull • RTMBdist

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

Usage

dziweibull(x, shape, scale, zeroprob = 0, log = FALSE)

pziweibull(q, shape, scale, zeroprob = 0, lower.tail = TRUE, log.p = FALSE)

rziweibull(n, shape, scale, zeroprob = 0)

Arguments

x, q: vector of quantiles
shape: positive shape parameter
scale: positive scale parameter
zeroprob: zero-inflation probability between 0 and 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

dziweibull gives the density, pziweibull gives the distribution function, and rziweibull generates random deviates.

Details

This implementation allows for automatic differentiation with RTMB.

$$f(x;\,k,\lambda,p_0) = p_0\,\mathbf{1}[x=0] + (1-p_0)\,f_{\mathrm{Weibull}}(x;\,k,\lambda)\,\mathbf{1}[x>0],$$ where $p_0$ is zeroprob, $k$ = shape, $\lambda$ = scale.

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.

Examples

x <- rziweibull(1, 1, 1, 0.5)
d <- dziweibull(x, 1, 1, 0.5)
p <- pziweibull(x, 1, 1, 0.5)