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Dataplot Vol 2 Vol 1

TRACDF

Name:
    TRACDF (LET)
Type:
    Library Function
Purpose:
    Compute the trapezoidal cumulative distribution function.
Description:
    The trapezoidal distribution has the following cumulative distribution function:

      F(x|a,b,c,d) = 0                                        x < a;
              = ((b-a)/(d+c-b-a))*((x-a)/(b-a))**2       a <= x < b;
              = ((b-a) + 2*(x-b))/(d+c-b-a)              b <= x < c;
              = 1 - ((d-c)/(d+c-b-a))*((d-x)/(d-c))**2   c <= x < d;
              = 1                                        x >= d
Syntax:
    LET <y> = TRACDF(<x>,<a>,<b>,<c> <d>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <x> is a variable, number, or parameter containing values in the interval (a,d);
                <a> is a number, parameter, or variable that specifies the first shape parameter;
                <b> is a number, parameter, or variable that specifies the second shape parameter;
                <c> is a number, parameter, or variable that specifies the third shape parameter;
                <d> is a number, parameter, or variable that specifies the fourth shape parameter;
                <y> is a variable or a parameter (depending on what <x> is) where the computed cdf value is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = TRACDF(0.5,0,0.25,0.75,1)
    LET A = TRACDF(0.5,A,B,C,D)
Default:
    None
Synonyms:
    None
Related Commands:
    TRAPDF = Compute the trapezoidal probability density function.
    TRAPPF = Compute the trapezoidal percent point function.
    TRIPDF = Compute the triangular probability density function.
    UNIPDF = Compute the uniform probability density function.
    SEMPDF = Compute the semi-circular probability density function.
    NORPDF = Compute the normal probability density function.
Reference:
    "Generalized Trapezoidal Distributions", van Dorp and Kotz, Metrika, Vol. 58, Issue 1, July, 2003.
Applications:
    Distributional Modeling
Implementation Date:
    2004/1
Program:
     
    TITLE TRAPEZOIDAL DISTRIBUTION
    LET A = 0
    LET B = 1
    LET C = 5
    LET D = 10
    PLOT TRACDF(X,A,B,C,D) FOR X = A 0.1 10
        
    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.