dist_student_t {distributional} | R Documentation |
The (non-central) location-scale Student t Distribution
Description
The Student's T distribution is closely related to the Normal()
distribution, but has heavier tails. As increases to
,
the Student's T converges to a Normal. The T distribution appears
repeatedly throughout classic frequentist hypothesis testing when
comparing group means.
Usage
dist_student_t(df, mu = 0, sigma = 1, ncp = NULL)
Arguments
df |
degrees of freedom ( |
mu |
The location parameter of the distribution.
If |
sigma |
The scale parameter of the distribution. |
ncp |
non-centrality parameter |
Details
We recommend reading this documentation on https://pkg.mitchelloharawild.com/distributional/, where the math will render nicely.
In the following, let be a central Students T random variable
with
df
= .
Support: , the set of all real numbers
Mean: Undefined unless , in which case the mean is
zero.
Variance:
Undefined if , infinite when
.
Probability density function (p.d.f):
See Also
Examples
dist <- dist_student_t(df = c(1,2,5), mu = c(0,1,2), sigma = c(1,2,3))
dist
mean(dist)
variance(dist)
generate(dist, 10)
density(dist, 2)
density(dist, 2, log = TRUE)
cdf(dist, 4)
quantile(dist, 0.7)