VGAM: zipoisUC – R documentation

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zipoisUC

Zero-Inflated Poisson Distribution

Description

Density, distribution function, quantile function and random generation for the zero-inflated and zero-deflated Poisson distribution with parameter pstr0.

Usage

dzipois(x, lambda, pstr0 = 0, log = FALSE)
pzipois(q, lambda, pstr0 = 0)
qzipois(p, lambda, pstr0 = 0)
rzipois(n, lambda, pstr0 = 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.
`pstr0`	Probability of a structural zero (i.e., ignoring the Poisson distribution), called phi. The default value of phi = 0 corresponds to the response having an ordinary Poisson distribution. This argument may be negative to allow for 0-deflation, hence its interpretation as a probability ceases.
`log`	Logical. Return the logarithm of the answer?

Details

The probability function of Y is 0 with probability phi, and Poisson(lambda) with probability 1-phi. Thus

P(Y=0) = phi + (1-phi) * P(W=0)

where W is distributed Poisson(lambda).

Value

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

Note

The argument pstr0 is recycled to the required length, and must have values which lie in the interval [0,1].

These functions actually allow for the zero-deflated Poisson distribution. Here, pstr0 is also permitted to lie in the interval [-1/expm1(lambda), 0]. The resulting probability of a zero count is less than the nominal Poisson value, and the use of pstr0 to stand for the probability of a structural zero loses its meaning. When pstr0 equals -1/expm1(lambda) this corresponds to the positive-Poisson distribution (e.g., see Gaitpois).

Author(s)

T. W. Yee

Examples

lambda <- 3; pstr0 <- 0.2; x <- (-1):7
(ii <- dzipois(x, lambda, pstr0 = pstr0))
max(abs(cumsum(ii) - pzipois(x, lambda, pstr0 = pstr0)))  # Should be 0
table(rzipois(100, lambda, pstr0 = pstr0))

table(qzipois(runif(100), lambda, pstr0))
round(dzipois(0:10, lambda, pstr0 = pstr0) * 100)  # Should be similar

## Not run:  x <- 0:10
par(mfrow = c(2, 1))  # Zero-inflated Poisson
barplot(rbind(dzipois(x, lambda, pstr0 = pstr0), dpois(x, lambda)),
        beside = TRUE, col = c("blue", "orange"),
        main = paste("ZIP(", lambda, ", pstr0 = ", pstr0, ") (blue) vs",
                     " Poisson(", lambda, ") (orange)", sep = ""),
        names.arg = as.character(x))

deflat.limit <- -1 / expm1(lambda)  # Zero-deflated Poisson
newpstr0 <- round(deflat.limit / 1.5, 3)
barplot(rbind(dzipois(x, lambda, pstr0 = newpstr0),
                dpois(x, lambda)),
        beside = TRUE, col = c("blue","orange"),
        main = paste("ZDP(", lambda, ", pstr0 = ", newpstr0, ") (blue) vs",
                     " Poisson(", lambda, ") (orange)", sep = ""),
        names.arg = as.character(x)) 
## End(Not run)

VGAM

Vector Generalized Linear and Additive Models

v1.1-5

GPL-3

Authors

Thomas Yee [aut, cre], Cleve Moler [ctb] (author of several LINPACK routines)

Initial release

2021-01-13