LogStudentT: Log-Student t Distribution

In TesiproV: Reliability Analysis Methods for Structural Engineering

Log-Student t Distribution

Description

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

Usage

dlt(x, hyper.param)

plt(q, hyper.param)

qlt(p, hyper.param)

rlt(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{\ln X - m}{s} \sqrt{\frac{n}{n+1}} \right),

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

The log-Student t distribution arises as the marginal distribution of a log-normal distributed variable with conjugate log-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.jcss-lc.org/publications/jcsspmc/concrete.pdf

Value

• dlt() returns the density.

• plt() returns the distribution function.

• qlt() returns the quantile function.

• rlt() 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(3.4, 0.14, 3, 10)
dlt(0.5, hp)

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