 Dataplot Vol 2 Vol 1

# FTCDF

Name:
FTCDF (LET)
Type:
Library Function
Purpose:
Compute the folded t cumulative distribution function with degrees of freedom. The degrees of freedom parameter should be a positive integer.
Description:
The folded t distribution is the absolute value of the t distribution. For details of the t distribution, enter HELP TPDF.

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.

Syntax:
LET <y> = FTCDF(<x>,<nu>)             <SUBSET/EXCEPT/FOR qualification>
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.
Examples:
LET A = FTCDF(3,10)
LET Y2 = FTCDF(X1,10)
LET Y = FTCDF(X,10) SUBSET X > 2
PLOT FTCDF(X,3) FOR X = 0.01 0.01 10
Default:
None
Synonyms:
None
Related Commands:
 FTPDF = Compute the folded t probability density 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.
Reference:
"Continuous Univariate Distributions, Volume 1", Second Edition, Johnson, Kotz, and Balakrishnan, Wiley, 1994, p. 403.
Applications:
Distributional Modeling
Implementation Date:
2004/1
Program:
```
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
Last updated: 2/3/2004