StudentT: Student t Distribution

In TesiproV: Reliability Analysis Methods for Structural Engineering

Student t Distribution

Description

Density, distribution function, quantile function and random generation for the Student t distribution.

Usage

dst(x, hyper.param)

pst(q, hyper.param)

qst(p, hyper.param)

rst(n_vals, hyper.param)

Arguments

x, q	Vector of quantiles.
hyper.param	Numeric vector (m, s, n, \nu).
p	Vector of probabilities.
n_vals	Number of random values to generate.

Details

The cumulative distribution function is given by

F_X(x) = F_{t_{\nu}}\left( \frac{x-m}{s} \sqrt{\frac{n}{n+1}} \right),

where F_{t_{\nu}}(\cdot) denotes the cumulative distribution function of a Student t distribution with \nu degrees of freedom.

The Student t distribution arises as the marginal distribution of a normal distributed variable with conjugate normal-gamma prior uncertainty in m and s.

The hyperparameter vector hyper.param is defined as

(m, s, n, \nu)

where

• m is the mean value of an equivalent sample of size n,

• s is the empirical standard deviation of an equivalent sample of size \nu + 1,

• \nu denotes the degrees of freedom of the Student t distribution.

For details see: https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/TDist

Value

• dst() returns the density.

• pst() returns the distribution function.

• qst() returns the quantile function.

• rst() generates random deviates.

Author(s)

(C) 2021-2026 K. Nille-Hauf, T. Feiri, M. Ricker, T. Lux – Hochschule Biberach (until 2022), TU Dortmund University - Chair of Structural Concrete (since 2023)

Examples

hp <- c(40, 4, 3, 10)
dst(0.5, hp)

TesiproV documentation built on Oct. 28, 2026, 5:13 p.m.