VGAM (version 1.1-9)

Zapois: Zero-Altered Poisson Distribution

Description

Density, distribution function, quantile function and random generation for the zero-altered Poisson distribution with parameter pobs0.

Usage

dzapois(x, lambda, pobs0 = 0, log = FALSE)
pzapois(q, lambda, pobs0 = 0)
qzapois(p, lambda, pobs0 = 0)
rzapois(n, lambda, pobs0 = 0)

Value

dzapois gives the density,

pzapois gives the distribution function,

qzapois gives the quantile function, and

rzapois generates random deviates.

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. If length(n) > 1 then the length is taken to be the number required.

lambda

Vector of positive means.

pobs0

Probability of zero, called \(pobs0\). The default value of pobs0 = 0 corresponds to the response having a positive Poisson distribution.

log

Logical. Return the logarithm of the answer?

Author

T. W. Yee

Details

The probability function of \(Y\) is 0 with probability pobs0, else a positive \(Poisson(\lambda)\).

See Also

zapoisson, Gaitdpois, dzipois.

Examples

lambda <- 3; pobs0 <- 0.2; x <- (-1):7
(ii <- dzapois(x, lambda, pobs0))
max(abs(cumsum(ii) - pzapois(x, lambda, pobs0)))  # Should be 0
table(rzapois(100, lambda, pobs0))
table(qzapois(runif(100), lambda, pobs0))
round(dzapois(0:10, lambda, pobs0) * 100)  # Should be similar

if (FALSE)  x <- 0:10
barplot(rbind(dzapois(x, lambda, pobs0), dpois(x, lambda)),
        beside = TRUE, col = c("blue", "green"), las = 1,
        main = paste0("ZAP(", lambda, ", pobs0 = ", pobs0, ") [blue]",
                      "vs Poisson(", lambda, ") [green] densities"),
        names.arg = as.character(x), ylab = "Probability")