DiscreteGamma: Discrete gamma distribution

Description

Probability mass function, distribution function and random generation for discrete gamma distribution.

Usage

ddgamma(x, shape, rate = 1, scale = 1/rate, log = FALSE)
pdgamma(q, shape, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)
rdgamma(n, shape, rate = 1, scale = 1/rate)

Arguments

x, q: vector of quantiles.
shape, scale: shape and scale parameters. Must be positive, scale strictly.
rate: an alternative way to specify the scale.
log, log.p: logical; if TRUE, probabilities p are given as log(p).
lower.tail: logical; if TRUE (default), probabilities are \(P[X \le x]\) otherwise, \(P[X > x]\).
n: number of observations. If length(n) > 1, the length is taken to be the number required.

Details

Probability mass function of discrete gamma distribution \(f_Y(y)\) is defined by discretization of continuous gamma distribution \(f_Y(y) = S_X(y) - S_X(y+1)\) where \(S_X\) is a survival function of continuous gamma distribution.

References

Chakraborty, S. and Chakravarty, D. (2012). Discrete Gamma distributions: Properties and parameter estimations. Communications in Statistics-Theory and Methods, 41(18), 3301-3324.

Examples

Run this code


x <- rdgamma(1e5, 9, 1)
xx <- 0:50
plot(prop.table(table(x)))
lines(xx, ddgamma(xx, 9, 1), col = "red")
hist(pdgamma(x, 9, 1))
plot(ecdf(x))
xx <- seq(0, 50, 0.1)
lines(xx, pdgamma(xx, 9, 1), col = "red", lwd = 2, type = "s")