dt(x, df, log=F) pt(q, df) qt(p, df) rt(n, df, bigdata=F)
bdVector of quantiles.
Missing values (
NAs) are allowed.
bdVector of 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.
bdVector of degrees of freedom.
This is replicated to be the same length as
p or
q or the number of
deviates generated.
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,
dt will return
the log of the density, not the density itself.
dt),
probability (
pt),
quantile (
qt), or
random sample (
rt)
for Student's
t-distribution on
df degrees of freedom.
rt 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 cause the corresponding
elements of the result to be missing.
A noncentral
t is the distribution of
(Z + d) / sqrt( chi^2 / df )
where
Z is standard normal,
d is the noncentrality parameter, and
df is the degrees of freedom of the
chi^2 variable.
To generate from the noncentral t, use
rnorm(n, d) / sqrt(rchisq(n, df=df) / df)
Note - with
d=0 this generates a different sequence of
random numbers than does
rt(). If consistency is important then use this procedure
instead of
rt() even when
d=0.
Student's t is a real valued distribution symmetric about 0. The t approaches the Gaussian (normal) distribution as the degrees of freedom go to infinity. The major use of the t is to test hypotheses and construct confidence intervals for means of Gaussian data.
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. 2. Houghton-Mifflin, Boston.
(1 - pt(1.96, 12))*2 # two-tailed p-value for t with 12 df