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 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 = b has density

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

for x > 0, a > 0 and b > 0.

Value

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

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))

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