halft1.mle: MLE of the half t distribution

In foldedt: The Folded t Family of Distributions

MLE of the half t distribution

Description

MLE of the half t distribution with unit scatter parameter.

Usage

halft1.mle(x, tol = 1e-07)

Arguments

x	A numerical vector with positive real numbers.
tol	The tolerance level up to which the maximisation stops set to 1e-07 by default.

Details

The half-t distribution with \nu > 0 degrees of freedom, zero location parameter and unit scatter parameter has density:

f(x) = \frac{2\Gamma\left(\frac{\nu+1}{2}\right)}{\sqrt{\nu\pi}\,\Gamma\left(\frac{\nu}{2}\right)} \left(1 + \frac{x^2}{\nu}\right)^{-\frac{\nu+1}{2}}, \quad x \geq 0.

Value

A list including:

iters	The number of iterations required by the Newton-Raphson algorithm.
nu	The estimated degrees of freedom of the half t distribution.
loglik	The value of the maximised log-likelihood.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

References

Psarakis and Panaretos (1990). The folded t distribution. Communications in Statistics–Theory and Methods, 19(7): 2717–2734.

https://en.wikipedia.org/wiki/Folded-t_and_half-t_distributions

See Also

halft.mle, dfoldedt

Examples

x <- abs( rt(1000, 5) )
halft.mle(x)

foldedt documentation built on March 21, 2026, 5:06 p.m.