GammaDist {base} | R Documentation |
Density, distribution function, quantile function and random
generation for the Gamma distribution with parameters shape
and
scale
.
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)
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]. |
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.
dgamma
gives the density,
pgamma
gives the distribution function
qgamma
gives the quantile function, and
rgamma
generates random deviates.
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)
.
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.
-log(dgamma(1:4, shape=1)) p <- (1:9)/10 pgamma(qgamma(p,shape=2), shape=2) 1 - 1/exp(qgamma(p, shape=1))