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)

Arguments

x, q

vector of quantiles.

vector of probabilities.

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?

Value

dzapois gives the density, pzapois gives the distribution function, qzapois gives the quantile function, and rzapois generates random deviates.

Details

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

Examples

Run this code

# NOT RUN {
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

# }
# NOT RUN {
 x <- 0:10
barplot(rbind(dzapois(x, lambda, pobs0), dpois(x, lambda)),
        beside = TRUE, col = c("blue", "green"), las = 1,
        main = paste("ZAP(", lambda, ", pobs0 = ", pobs0, ") [blue] vs",
                   " Poisson(", lambda, ") [green] densities", sep = ""),
        names.arg = as.character(x), ylab = "Probability") 
# }