dist_student_t
The (non-central) location-scale Student t Distribution
Description
![[Stable]](../help/figures/lifecycle-stable.svg)
Usage
dist_student_t(df, mu = 0, sigma = 1, ncp = NULL)
Arguments
df |
degrees of freedom (> 0, maybe non-integer). |
mu |
The location parameter of the distribution.
If |
sigma |
The scale parameter of the distribution. |
ncp |
non-centrality parameter delta;
currently except for |
Details
The Student's T distribution is closely related to the Normal()
distribution, but has heavier tails. As ν increases to ∞,
the Student's T converges to a Normal. The T distribution appears
repeatedly throughout classic frequentist hypothesis testing when
comparing group means.
We recommend reading this documentation on https://pkg.mitchelloharawild.com/distributional/, where the math will render nicely.
In the following, let X be a central Students T random variable
with df = ν.
Support: R, the set of all real numbers
Mean: Undefined unless ν ≥ 2, in which case the mean is zero.
Variance:
ν / (ν - 2)
Undefined if ν < 1, infinite when 1 < ν ≤ 2.
Probability density function (p.d.f):
f(x) = Γ((ν + 1) / 2) / (√(ν π) Γ(ν / 2)) (1 + x^2 / ν)^(- (ν + 1) / 2)
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)