GammaDist                package: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 <= x],
          otherwise, P[X > x].

Details:

     If `scale' is omitted, it assumes the default value of `1'.

     The Gamma distribution with parameters `shape' = a and `scale' = s
     has density

               f(x)= 1/(s^a Gamma(a)) x^(a-1) e^-(x/s)

     for x > 0, a > 0 and s > 0. The mean and variance are E(X) = a*s
     and Var(X) = a*s^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))

