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.


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]




Relation to other distributionsEdit

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 and half-Cauchy distributions for  .

See alsoEdit


  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 readingEdit

External linksEdit

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