Zero-Altered Poisson Distribution

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.

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?

Details

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

Value

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

Author

T. W. Yee

Note

The argument pobs0 is recycled to the required length, and must have values which lie in the interval \([0,1]\).

Examples

lambda <- 3; pobs0 <- 0.2; x <- (-1):7
(ii <- dzapois(x, lambda, pobs0))
#> [1] 0.00000000 0.20000000 0.12574967 0.18862451 0.18862451 0.14146838 0.08488103
#> [8] 0.04244051 0.01818879
max(abs(cumsum(ii) - pzapois(x, lambda, pobs0)))  # Should be 0
#> [1] 1.110223e-16
table(rzapois(100, lambda, pobs0))
#> 
#>  0  1  2  3  4  5  6  7 10 
#> 17 13 22 23 14  3  4  3  1 
table(qzapois(runif(100), lambda, pobs0))
#> 
#>  0  1  2  3  4  5  6  7  8 
#> 14 16 16 13 19 12  8  1  1 
round(dzapois(0:10, lambda, pobs0) * 100)  # Should be similar
#>  [1] 20 13 19 19 14  8  4  2  1  0  0

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")  # \dontrun{}