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, rate = 1, scale = 1/rate, log = FALSE)
pgamma(q, shape, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)
qgamma(p, shape, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)
rgamma(n, shape, rate = 1, scale = 1/rate)

Arguments

x, q	vector of quantiles.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.
rate	an alternative way to specify the scale.
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 P[X \le x], otherwise, P[X > x].

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. The mean and variance are E(X) = \alpha\sigma and Var(X) = \alpha\sigma^2.

Value

dgamma gives the density, pgamma gives the distribution function qgamma gives the quantile function, and rgamma generates random deviates.

Note

The S parametrization is via shape and rate: S has no scale parameter. Prior to 1.4.0 R only had scale.

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-squared 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))

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