zipoisUC: Zero-Inflated Poisson Distribution

Description Usage Arguments Details Value Note Author(s) See Also Examples

Description

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

Usage

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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

See Also

zipoisson, Gaitpois, dpois, rzinegbin.

Examples

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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)

Example output

Loading required package: stats4
Loading required package: splines
[1] 0.00000000 0.23982965 0.11948896 0.17923345 0.17923345 0.13442508 0.08065505
[8] 0.04032753 0.01728323
[1] 3.330669e-16

 0  1  2  3  4  5  6  7 
26  9 17 19 14  6  7  2 

 0  1  2  3  4  5  6 
23 16 19 18 10  4 10 
 [1] 24 12 18 18 13  8  4  2  1  0  0

VGAM documentation built on Jan. 16, 2021, 5:21 p.m.