Probability mass function and random generation for the gamma-Poisson distribution.
dgpois(x, shape, rate, scale = 1/rate, log = FALSE)pgpois(q, shape, rate, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)
rgpois(n, shape, rate, scale = 1/rate)
vector of quantiles.
shape and scale parameters. Must be positive, scale strictly.
an alternative way to specify the scale.
logical; if TRUE, probabilities p are given as log(p).
logical; if TRUE (default), probabilities are
number of observations. If length(n) > 1
,
the length is taken to be the number required.
Gamma-Poisson distribution arises as a continuous mixture of
Poisson distributions, where the mixing distribution
of the Poisson rate
Probability mass function
Cumulative distribution function is calculated using recursive algorithm that employs the fact that
what makes recursive updating from
and let's us efficiently calculate cumulative distribution function as a sum of probability mass functions
x <- rgpois(1e5, 7, 0.002)
xx <- seq(0, 12000, by = 1)
hist(x, 100, freq = FALSE)
lines(xx, dgpois(xx, 7, 0.002), col = "red")
hist(pgpois(x, 7, 0.002))
xx <- seq(0, 12000, by = 0.1)
plot(ecdf(x))
lines(xx, pgpois(xx, 7, 0.002), col = "red", lwd = 2)
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