pospoisUC: Positive-Poisson Distribution

In VGAMdata: Data Supporting the 'VGAM' Package

Positive-Poisson Distribution

Description

Density, distribution function, quantile function and random generation for the positive-Poisson distribution.

Usage

dpospois(x, lambda, log = FALSE)
ppospois(q, lambda)
qpospois(p, lambda)
rpospois(n, lambda)

Arguments

x, q	vector of quantiles.
p	vector of probabilities.
n	number of observations. Fed into runif.
lambda	vector of positive means (of an ordinary Poisson distribution). Short vectors are recycled.
log	logical.

Details

The positive-Poisson distribution is a Poisson distribution but with the probability of a zero being zero. The other probabilities are scaled to add to unity. The mean therefore is

\lambda / (1-\exp(-\lambda)).

As \lambda increases, the positive-Poisson and Poisson distributions become more similar. Unlike similar functions for the Poisson distribution, a zero value of lambda returns a NaN.

Value

dpospois gives the density, ppospois gives the distribution function, qpospois gives the quantile function, and rpospois generates random deviates.

Note

These functions are or are likely to be deprecated. Use Gaitdpois instead.

The family function pospoisson estimates \lambda by maximum likelihood estimation.

Author(s)

T. W. Yee

See Also

Gaitdpois, pospoisson, zapoisson, zipoisson, rpois.

Examples

lambda <- 2; y = rpospois(n = 1000, lambda)
table(y)
mean(y)  # Sample mean
lambda / (1 - exp(-lambda))  # Population mean

(ii <- dpospois(0:7, lambda))
cumsum(ii) - ppospois(0:7, lambda)  # Should be 0s
table(rpospois(100, lambda))

table(qpospois(runif(1000), lambda))
round(dpospois(1:10, lambda) * 1000)  # Should be similar

## Not run:  x <- 0:7
barplot(rbind(dpospois(x, lambda), dpois(x, lambda)),
        beside = TRUE, col = c("blue", "orange"),
        main = paste("Positive Poisson(", lambda, ") (blue) vs",
        " Poisson(", lambda, ") (orange)", sep = ""),
        names.arg = as.character(x), las = 1, lwd = 2) 
## End(Not run)

VGAMdata documentation built on April 3, 2025, 6:49 p.m.