The folded t distribution provides an alternative to the half-normal or half-Cauchy in distributional modeling applications. A folded t with 1 degree of freedom is equivalent to a half-Cauchy and the folded t approximates the half-normal as the degrees of freedom gets large (in practice, the approximation is quite good for degrees of freedom > 30). Thus the folded t allows you to model with tails that can vary from normal to Cauchy in behavior.
where <y> is a variable or a parameter;
<x> is a variable or a parameter (depending on what <x> is) where the computed folded t pdf value is stored;
<NU> is a positive number or parameter that specifies the degrees of freedom;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET Y2 = FTPDF(X1,10)
LET Y = FTPDF(X,10) SUBSET X > 2
PLOT FTPDF(X,3) FOR X = 0.01 0.01 10
MULTIPLOT CORNER COORDINATES 0 0 100 100 MULTIPLOT SCALE FACTOR 2 MULTIPLOT 2 2 TITLE AUTOMATIC PLOT FTPDF(X,1) FOR X = 0 0.01 10 PLOT FTPDF(X,5) FOR X = 0 0.01 10 PLOT FTPDF(X,10) FOR X = 0 0.01 10 PLOT FTPDF(X,30) FOR X = 0 0.01 10 END OF MULTIPLOT
Date created: 2/3/2004