# DiscreteGamma: Discrete gamma distribution In extraDistr: Additional Univariate and Multivariate Distributions

## Description

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

## Usage

 ```1 2 3 4 5``` ```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 ≤ 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 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.

## References

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

`GammaDist`, `DiscreteNormal`
 ```1 2 3 4 5 6 7 8``` ```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") ```