The Zero-Inflated Poisson Distribution

Source: R/dpqr.R

Density, distribution function, quantile function and random generation for the zero-inflated Poisson (ZIP) distribution with parameters lambda and omega.

dzip(x, lambda, omega, log = FALSE)
pzip(q, lambda, omega, lower.tail = TRUE, log.p = FALSE)
qzip(p, lambda, omega, lower.tail = TRUE, log.p = FALSE)
rzip(n, lambda, omega)

Arguments

x, q

vector of quantiles.
p

vector of probabilities.
n

number of random values to return.
lambda

vector of (non-negative) means.
omega

zero-inflation parameter.
log, log.p

logical; if TRUE, probabilities p are given as log(p).
lower.tail

logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].

Value

dzip gives the density, pzip gives the distribution function, qzip gives the quantile function, and rzip generates random deviates.

See also

dzinb, pzinb, qzinb, and rzinb for the zero-inflated negative binomial (ZINB) distribution.

Examples

dzip(x = 0:10, lambda = 1, omega = 0.5)
#>  [1] 6.839397e-01 1.839397e-01 9.196986e-02 3.065662e-02 7.664155e-03
#>  [6] 1.532831e-03 2.554718e-04 3.649598e-05 4.561997e-06 5.068886e-07
#> [11] 5.068886e-08
pzip(q = c(1, 5, 9), lambda = 1, omega = 0.5)
#> [1] 0.8678794 0.9997029 0.9999999
qzip(p = c(0.25, 0.50, 0.75), lambda = 1, omega = 0.5)
#> [1] 0 0 1
set.seed(123)
rzip(n = 100, lambda = 1, omega = 0.5)
#>   [1] 1 0 1 0 0 2 0 0 0 0 0 0 0 0 1 0 1 3 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0
#>  [38] 2 3 1 0 1 0 0 2 0 0 0 0 0 2 1 0 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 2
#>  [75] 1 1 1 0 2 1 2 0 1 0 1 1 0 0 0 2 0 0 4 0 3 1 0 1 0 0