dgamma(x, shape, rate=1, scale, log=FALSE) pgamma(q, shape, rate=1, scale, lower.tail=TRUE, log.p=FALSE) qgamma(p, shape, rate=1, scale) rgamma(n, shape, rate=1, scale, bigdata=FALSE)
bdVector of (positive) quantiles.
Missing values (
NAs) are allowed.
bdVector of (positive) quantiles.
Missing values (
NAs) are allowed.
bdVector of probabilities.
Missing values (
NAs) are allowed.
length(n) is larger than 1, then
length(n) random values are returned.
p or
q or the number of
deviates generated.
shape/
rate, the variance is
shape/
rate^2, and the skewness is
2/sqrt(shape).
rate,
often called beta.
If
scale is supplied
and
rate is not, then
rate = 1/scale.
This is ignored if
rate is supplied.
TRUE, an object of type
bdVector is returned.
Otherwise, a
vector object is returned. This argument can be used only if the bigdata library section has been loaded.
TRUE,
dgamma will return
the log of the density, not the density itself.
TRUE,
pgamma(x) will return
P(X<=x), otherwise
P(X>x).
TRUE,
pgamma will return
the log of the probability, not the probability itself.
dgamma),
probability (
pgamma),
quantile (
qgamma), or
random sample (
rgamma)
for the gamma distribution with shape
shape.
rgamma causes creation of the dataset
.Random.seed if it does
not already exist, otherwise its value is updated.
Elements of
q or
p that are missing will cause the corresponding
elements of the result to be missing.
The gamma distribution takes values on the positive real line.
Special cases of the gamma
are the exponential distribution and the chi-squared distributions
(see
Exponential and
Chisquare). Applications of the gamma include
queuing theory, inventory control and precipitation processes.
For
shape less than
10^8
pgamma(q,shape)
is computed using formulae 6.5.31 and 6.5.32 of Abramowitz and Stegun (1970). For these values
of
shape
dgamma is computed based
on the
lgamma function. For larger
values of shape
pgamma and
dgamma use
a normal approximation, adjusted for skewness only. See formulae
26.2.48 and 26.1.32 of Abramowitz and Stegun. There may be slight discontinuities
in higher derivatives at
shape==10^8.
For details on the uniform random number generator implemented in S-PLUS,
see the
set.seed help file.
Johnson, N. L. and Kotz, S. (1970).
Continuous Univariate Distributions, vol. 1.
Houghton-Mifflin, Boston.
Gamma Distribution. In
Encyclopedia of Statistical Sciences.
S. Kotz and N. L. Johnson, eds.
See
family for the family generating function
Gamma used with the
glm
and
gam functions. See
gamma for the gamma function.
rgamma(20,10) # sample of 20 with shape parameter 10
pgamma(1.2, 1.5) # the probability that a value from the gamma
# distribution with shape 1.5 is less than 1.2
x <- qgamma(seq(.001, .999, len = 100), 1.5) # compute a vector of quantiles
# be sure that you have an open graphics window
plot(x, dgamma(x, 1.5), type = "l") # density plot for shape 1.5