Package 'foldedt'

The folded t family of distributions.

Description

Maximum likelihood estimation of the folded t and related distributions. Probability and density functions, and random generation are also included.

Details

Package:	foldedt
Type:	Package
Version:	1.0
Date:	2026-03-18
License:	GPL-2

Maintainers

Michail Tsagris [email protected].

Author(s)

Michail Tsagris [email protected].

References

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

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Density function of the (non-standardized) folded t distribution

Description

Density function of the (non-standardized) folded t distribution.

Usage

dfoldedt(y, mu, s2, v, logged = FALSE)

Arguments

y	A vector with positive values.
mu	The location parameter, $\mu$.
s2	The $\sigma^2$ parameter.
v	The degrees of freedom, $v$.
logged	If you want the logarithm of the density set this equal to TRUE.

Value

A vector with the (logged) density function values.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [email protected].

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

foldedt.mle

Examples

y <- abs( rt(10, 10, 3) )
dfoldedt(y, mu = 3, s2 = 1, v = 10)

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MLE of the folded t distribution

Description

MLE of the folded t distribution.

Usage

foldedt.mle(x)

Arguments

x	A numerical vector with positive real numbers.

Value

A list including:

param	The estimated location and scatter parameters, and the degrees of freedom of the folded t distribution.
loglik	The value of the maximised log-likelihood.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [email protected].

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, halft1.mle, dfoldedt

Examples

x <- abs( rt(1000, 5, 2) )
foldedt.mle(x)

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MLE of the half t distribution

Description

MLE of the half t distribution.

Usage

halft.mle(x)

Arguments

x	A numerical vector with positive real numbers.

Details

The half-t distribution with $\nu$ degrees of freedom and scatter parameter $\sigma > 0$ has density:

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

Value

A list including:

param	The estimated degrees of freedom and the scatter parameter of the half t distribution.
loglik	The value of the maximised log-likelihood.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [email protected].

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

halft1.mle

Examples

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

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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 [email protected].

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)

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