Zigeom: Zero-Inflated Geometric Distribution

Description

Density, and random generation for the zero-inflated geometric distribution with parameter pszero.

Usage

dzigeom(x, prob, pszero = 0, log = FALSE)
pzigeom(q, prob, pszero = 0)
qzigeom(p, prob, pszero = 0)
rzigeom(n, prob, pszero = 0)

Arguments

x, q

vector of quantiles.

vector of probabilities.

prob

see dgeom.

number of observations.

pszero

Probability of structural zero (ignoring the geometric distribution), called $\phi$. The default value corresponds to the response having an ordinary geometric distribution.

log

Logical. Return the logarithm of the answer?

Value

dzigeom gives the density, pzigeom gives the distribution function, qzigeom gives the quantile function, and rzigeom generates random deviates.

Details

The probability function of $Y$ is 0 with probability $\phi$, and $geometric(prob)$ with probability $1-\phi$. Thus $$P(Y=0) =\phi + (1-\phi) P(W=0)$$ where $W$ is distributed $geometric(prob)$.

Examples

Run this code

prob = 0.5; pszero = 0.2; x = (-1):20
(ii = dzigeom(x, prob, pszero))
max(abs(cumsum(ii) - pzigeom(x, prob, pszero))) # Should be 0
table(rzigeom(1000, prob, pszero))

x = 0:10
barplot(rbind(dzigeom(x, prob, pszero), dgeom(x, prob)),
        beside = TRUE, col = c("blue","orange"),
        ylab = "P[Y = y]", xlab = "y", las = 1,
        main = paste("zigeometric(", prob, ", pszero = ", pszero,
                     ") (blue) vs",
                     " geometric(", prob, ") (orange)", sep = ""),
        names.arg = as.character(x))