VGAM (version 0.9-0)

Zigeom: Zero-Inflated Geometric Distribution

Description

Density, and random generation for the zero-inflated geometric distribution with parameter pstr0.

Usage

dzigeom(x, prob, pstr0 = 0, log = FALSE)
pzigeom(q, prob, pstr0 = 0)
qzigeom(p, prob, pstr0 = 0)
rzigeom(n, prob, pstr0 = 0)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

prob

see dgeom.

n

number of observations.

pstr0

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 $geometric(prob)$.

See Also

zigeometric, dgeom.

Examples

prob <- 0.5; pstr0 <- 0.2; x <- (-1):20
(ii <- dzigeom(x, prob, pstr0))
max(abs(cumsum(ii) - pzigeom(x, prob, pstr0))) # Should be 0
table(rzigeom(1000, prob, pstr0))

x <- 0:10
barplot(rbind(dzigeom(x, prob, pstr0), dgeom(x, prob)),
        beside = TRUE, col = c("blue","orange"),
        ylab = "P[Y = y]", xlab = "y", las = 1,
        main = paste("zigeometric(", prob, ", pstr0 = ", pstr0,
                     ") (blue) vs",
                     " geometric(", prob, ") (orange)", sep = ""),
        names.arg = as.character(x))