The Zero-Inflated Negative Binomial Distribution

Source: R/dpqr.R

Density, distribution function, quantile function and random generation for the zero-inflated negative binomial (ZINB) distribution with parameters k, lambda, and omega.

dzinb(x, k, lambda, omega, log = FALSE)
pzinb(q, k, lambda, omega, lower.tail = TRUE, log.p = FALSE)
qzinb(p, k, lambda, omega, lower.tail = TRUE, log.p = FALSE)
rzinb(n, k, lambda, omega)

Arguments

x, q

vector of quantiles.
p

vector of probabilities.
n

number of random values to return.
k

dispersion parameter.
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

dzinb gives the density, pzinb gives the distribution function, qzinb gives the quantile function, and rzinb generates random deviates.

See also

dzip, pzip, qzip, and rzip for the zero-inflated Poisson (ZIP) distribution.

Examples

dzinb(x = 0:10, k = 1, lambda = 1, omega = 0.5)
#>  [1] 0.7500000000 0.1250000000 0.0625000000 0.0312500000 0.0156250000
#>  [6] 0.0078125000 0.0039062500 0.0019531250 0.0009765625 0.0004882813
#> [11] 0.0002441406
pzinb(q = c(1, 5, 9), k = 1, lambda = 1, omega = 0.5)
#> [1] 0.8750000 0.9921875 0.9995117
qzinb(p = c(0.25, 0.50, 0.75), k = 1, lambda = 1, omega = 0.5)
#> [1] 0 0 0
set.seed(123)
rzinb(n = 100, k = 1, lambda = 1, omega = 0.5)
#>   [1] 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 4 1 0
#>  [38] 1 1 0 0 1 4 0 1 6 1 2 0 0 0 0 0 1 0 0 0 0 0 3 0 1 0 0 0 1 0 0 0 4 0 0 0 0
#>  [75] 0 2 0 0 3 0 0 0 1 0 1 0 0 0 0 2 0 0 0 0 2 4 0 0 0 0