zipois: The Zero Inflated Poisson Distribution

In attrCUSUM: Tools for Attribute VSI CUSUM Control Chart

Description

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

Usage

dzipois(x, rho, lambda, log = FALSE)

pzipois(q, rho, lambda, lower.tail = TRUE, log.p = FALSE)

qzipois(p, rho, lambda, lower.tail = TRUE, log.p = FALSE)

rzipois(n, rho, lambda)

Arguments

x	A non-negative integer-valued vector of quantiles.
q	A numeric vector of quantiles.
p	A vector of probabilities.
n	Number of random values to return, a length-one positive integer-valued vector.
rho	A length-one vector of zero inflation parameter on [0,1].
lambda	A length-one vector of positive means.
log, log.p	A length-one logical vector; if TRUE, probabilities p are given as log(p).
lower.tail	A length-one logical vector; if TRUE (the default), probabilities are P(X ≤ x), otherwise, P(X > x).

Details

The probability mass function of X is given by

P(X=x) = rho I(x = 0) + (1 - rho) P(Y=x), x=0,1,2,...,

where Y is distributed Poisson(lambda).

Value

dzipois gives the (log) density, pzipois gives the (log) distribution function, qzipois gives the quantile function, and rzipois generates random deviates.

Invalid arguments rise an error with a helpful message.

References

Lambert, D. (1992). Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing, Technometrics, 34(1), 1-14.

See Also

Poisson for the Poisson distribution.

Examples

# Example 1: dzipois
dzipois(x = 0:10, rho = 0.1, lambda = 5)

# Example 2: pzipois
pzipois(q = 2, rho = 0.1, lambda = 5)

# Example 3: qzipois
qzipois(p = pzipois(2, 0.1, 5), rho = 0.1, lambda = 5)

# Example 4: rzipois
n <- 1e+5
rho <- 0.2
lambda <- 5
mean(rzipois(n, rho, lambda)) # Sample mean
lambda * (1 - rho) # Theoretical mean

Example output

 [1] 0.10606415 0.03032076 0.07580190 0.12633651 0.15792063 0.15792063
 [7] 0.13160053 0.09400038 0.05875024 0.03263902 0.01631951
[1] 0.2121868
[1] 2
[1] 4.00825
[1] 4

attrCUSUM documentation built on May 2, 2019, 9:25 a.m.