DiscreteGamma {extraDistr}

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.

See Also

GammaDist, DiscreteNormal

Examples

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")