Discrete gamma distribution
Probability mass function, distribution function and random generation for discrete gamma distribution.
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)
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 ≤ x] otherwise, P[X > x]. |
n |
number of observations. If |
Probability mass function of discrete gamma distribution f is defined by discretization of continuous gamma distribution f(y) = S(x) - S(x+1) where S is a survival function of continuous gamma distribution.
Chakraborty, S. and Chakravarty, D. (2012). Discrete Gamma distributions: Properties and parameter estimations. Communications in Statistics-Theory and Methods, 41(18), 3301-3324.
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")
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