Density, cumulative probability, quantiles and random generation for
Student's t distribution.
USAGE:
dt(x, df)
pt(q, df)
qt(p, df)
rt(n, df)
REQUIRED ARGUMENTS:
x:
vector of quantiles.
Missing values (NAs) are allowed.
q:
vector of quantiles.
Missing values (NAs) are allowed.
p:
vector of probabilities.
Missing values (NAs) are allowed.
n:
sample size.
If length(n) is larger than 1, then length(n) random values are returned.
df:
vector of degrees of freedom.
This is replicated to be the same length as p or q or the number of
deviates generated.
VALUE:
density (dt),
probability (pt),
quantile (qt), or
random sample (rt)
for Student's
t-distribution on df degrees of freedom.
SIDE EFFECTS:
The function rt causes creation of the dataset .Random.seed if it does
not already exist, otherwise its value is updated.
DETAILS:
Elements of q or p that are missing will cause the corresponding
elements of the result to be missing.
BACKGROUND:
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.
REFERENCES:
Johnson, N. L. and Kotz, S. (1970).
Continuous Univariate Distributions, vol. 2.
Houghton-Mifflin, Boston.