| GammaDist {base} | R Documentation |
The Gamma Distribution
Description
Density, distribution function, quantile function and random
generation for the Gamma distribution with parameters shape and
scale.
Usage
dgamma(x, shape, scale=1, log = FALSE)
pgamma(q, shape, scale=1, lower.tail = TRUE, log.p = FALSE)
qgamma(p, shape, scale=1, lower.tail = TRUE, log.p = FALSE)
rgamma(n, shape, scale=1)
Arguments
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. |
shape, scale |
shape and scale parameters. |
log, log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are
|
Details
If scale is omitted, it assumes the default value of 1.
The Gamma distribution with parameters shape =\alpha
and scale =\sigma has density
f(x) = \frac{1}{{\sigma}^{\alpha}\Gamma(\alpha)} {x}^{\alpha-1} e^{-x/\sigma}%
for x > 0, \alpha > 0 and \sigma > 0.
Value
dgamma gives the density,
pgamma gives the distribution function
qgamma gives the quantile function, and
rgamma generates random deviates.
Note
The cumulative hazard H(t) = - \log(1 - F(t))
is -pgamma(t, ..., lower = FALSE, log = TRUE).
See Also
gamma for the Gamma function, dbeta for
the Beta distribution and dchisq for the chi-square
distribution which is a special case of the Gamma distribution.
Examples
-log(dgamma(1:4, shape=1))
p <- (1:9)/10
pgamma(qgamma(p,shape=2), shape=2)
1 - 1/exp(qgamma(p, shape=1))