VGAM (version 0.7-2)

Zipois: Zero-Inflated Poisson Distribution

Description

Density, distribution function, quantile function and random generation for the zero-inflated Poisson distribution with parameter phi.

Usage

dzipois(x, lambda, phi = 0)
pzipois(q, lambda, phi = 0)
qzipois(p, lambda, phi = 0)
rzipois(n, lambda, phi = 0)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. Must be a single positive integer.

lambda

Vector of positive means.

phi

Probability of zero (ignoring the Poisson distribution), called $\phi$. The default value of $\phi=0$ corresponds to the response having an ordinary Poisson distribution.

Value

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

Details

The probability function of $Y$ is 0 with probability $\phi$, and $Poisson(\lambda)$ with probability $1-\phi$. Thus $$P(Y=0)=\varphi +(1-\varphi )P(W=0)$$ where $W$ is distributed $Poisson(\lambda)$.

See Also

dpois, zipoisson.

Examples

lambda = 4
phi = 0.8
(i = dzipois(0:7, lambda, phi))
cumsum(i) - pzipois(0:7, lambda, phi)  # Should be 0s
table(rzipois(100, lambda, phi))

table(qzipois(runif(100), lambda, phi))
round(dzipois(0:10, lambda, phi) * 100) # Should be similar

x = 0:10
plot(x, dzipois(x, lambda, phi), type="h", ylab="Probability", 
     main=paste("ZIP(", lambda, ", phi=", phi, ") (blue) vs",
     " Poisson(", lambda, ") (red and shifted slightly)", sep=""),
     lwd=2, col="blue", las=1)
lines(x+0.05, dpois(x, lambda), type="h", lwd=2, col="red")