Folded-t and half-t distributions
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:
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
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 .
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