Folded-t and half-t distributions

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In statistics, the folded-t and half-t distributions are derived from Student's t-distribution by taking the absolute values of variates. This is analogous to the folded-normal and the half-normal statistical distributions being derived from the normal distribution.

Definitions[]

The folded non-standardized t distribution is the distribution of the absolute value of the non-standardized t distribution with degrees of freedom; its probability density function is given by:[citation needed]

.

The half-t distribution results as the special case of , and the standardized version as the special case of .

If , the folded-t distribution reduces to the special case of the half-t distribution. Its probability density function then simplifies to

.

The half-t distribution's first two moments (expectation and variance) are given by:[1]

,

and

.

Relation to other distributions[]

Folded-t and half-t generalize the folded normal and half-normal distributions by allowing for finite degrees-of-freedom (the normal analogues constitute the limiting cases of infinite degrees-of-freedom). Since the Cauchy distribution constitutes the special case of a Student-t distribution with one degree of freedom, the families of folded and half-t distributions include the folded Cauchy distribution and half-Cauchy distributions for .

See also[]

  • Modified half-normal distribution

References[]

  1. ^ Psarakis, S.; Panaretos, J. (1990), "The folded t distribution", Communications in Statistics - Theory and Methods, 19 (7): 2717–2734, doi:10.1080/03610929008830342

Further reading[]

  • Psarakis, S.; Panaretos, J. (1990). "The folded t distribution". Communications in Statistics - Theory and Methods. 19 (7): 2717–2734. doi:10.1080/03610929008830342.
  • Gelman, A. (2006). "Prior distributions for variance parameters in hierarchical models". Bayesian Analysis. 1 (3): 515–534.
  • Röver, C.; Bender, R.; Dias, S.; Schmid, C.H.; Schmidli, H.; Sturtz, S.; Weber, S.; Friede, T. (2020), On weakly informative prior distributions for the heterogeneity parameter in Bayesian random-effects meta-analysis, arXiv:2007.08352
  • Wiper, M. P.; Girón, F. J.; Pewsey, Arthur (2008). "Objective Bayesian Inference for the Half-Normal and Half-t Distributions". Communications in Statistics - Theory and Methods. 37 (20): 3165–3185. doi:10.1080/03610920802105184.
  • Tancredi, A. (2002). "Accounting for heavy tails in stochastic frontier models". Working paper (7325). Università degli Studi di Padova. Cite journal requires |journal= (help)

External links[]

  • Functions to evaluate half-t distributions are available in several R packages, e.g. [1] [2] [3].


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