TITLE(GammaDist @@ The Gamma Distribution)
USAGE(
dgamma(x, shape, scale=1)
pgamma(q, shape, scale=1)
qgamma(p, shape, scale=1)
rgamma(n, shape, scale=1)
)
ALIAS(dgamma)
ALIAS(pgamma)
ALIAS(qgamma)
ALIAS(rgamma)
ARGUMENTS(
ARG(x,q @@ vector of quantiles.)
ARG(p @@ vector of probabilites.)
ARG(n @@ number of observations.)
ARG(shape, scale @@ shape and scale parameters.)
)
VALUE(
These functions provide information about the gamma
distribution with parameters LANG(shape) and LANG(scale).
LANG(dgamma) gives the density,
LANG(pgamma) gives the distribution function
LANG(qgamma) gives the quantile function
and
LANG(rgamma) generates random deviates.
PARA
The gamma distribution with parameters LANG(shape) EQN(EQUALS a @@ = a) and
LANG(scale) EQN(EQUALS b @@ = b) has density
DEQN(f(x) =
OVER(1 @@ SUP(b@@a) greekGamma (a)) SUP(x@@a-1) SUP(e@@-x/b)
@@
f(x) = 1/(b^a Gamma(a)) x^(a-1) e^-(x/b))
for EQN(x GT 0 @@ x > 0),
EQN(a GT 0 @@ a > 0)
and
EQN(b GT 0 @@ b > 0).
)
SEEALSO(
LANG(LINK(gamma)), LANG(LINK(dbeta)).
)
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))
)
KEYWORD(distribution)
