FTPDF

FTPDF (LET)

Library Function

Compute the folded t probability density function with degrees of freedom. The degrees of freedom parameter should be a positive integer.

The folded t distribution is the absolute value of the t distribution. For details of the t distribution, enter HELP TPDF.

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.

LET <y> = FTPDF(<x>,NU)             <SUBSET/EXCEPT/FOR qualification>
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 A = FTPDF(3,10)
LET Y2 = FTPDF(X1,10)
LET Y = FTPDF(X,10) SUBSET X > 2
PLOT FTPDF(X,3) FOR X = 0.01 0.01 10

None

None

FTCDF	= Compute the folded t cumulative distribution function.
FTPPF	= Compute the folded t percent point function.
TPDF	= Compute the t probability density function.
STPDF	= Compute the skewed t probability density function.
HFNPDF	= Compute the half-normal probability density function.
FNRPDF	= Compute the folded normal probability density function.
HFCPDF	= Compute the half-Cauchy probability density function.

"Continuous Univariate Distributions, Volume 2", Second Edition, Johnson, Kotz, and Balakrishnan, Wiley, 1994, p. 403.

Distributional Modeling

2004/1

 
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