The folded t cumulative distribution function is computed using the t cumulative distribution as follows:
with tcdf denoting the t cumulative distribution function and denoting the shape parameter.
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 half-normal to half-Cauchy in behavior.
where <x> is a variable or a parameter;
<y> is a variable or a parameter (depending on what <x> is) where the computed folded t cdf 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 = FTCDF(X1,10)
LET Y = FTCDF(X,10) SUBSET X > 2
PLOT FTCDF(X,3) FOR X = 0.01 0.01 10
MULTIPLOT CORNER COORDINATES 0 0 100 100 MULTIPLOT SCALE FACTOR MULTIPLOT 2 2 TITLE AUTOMATIC PLOT FTCDF(X,1) FOR X = 0 0.01 10 PLOT FTCDF(X,5) FOR X = 0 0.01 10 PLOT FTCDF(X,10) FOR X = 0 0.01 10 PLOT FTCDF(X,30) FOR X = 0 0.01 10 END OF MULTIPLOT
Date created: 2/3/2004