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Dataplot Vol 2 Vol 1

FTCDF

Name:
    FTCDF (LET)
Type:
    Library Function
Purpose:
    Compute the folded t cumulative distribution function with NU 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:

      FTCDF(x,nu) = 2*TCDF(x,nu) - 1.0

    with tcdf denoting the t cumulative distribution function and NU 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
        
    plot generated by sample program

Date created: 2/3/2004
Last updated: 2/3/2004
Please email comments on this WWW page to alan.heckert@nist.gov.