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Dataplot Vol 2 Vol 1

TOPCDF

Name:
    TOPCDF (LET)
Type:
    Library Function
Purpose:
    Compute the Topp and Leone cumulative distribution function with shape parameter beta.
Description:
    The standard Topp and Leone distribution has the following cumulative distribution function:

      F(x;beta) = (2*x - x**2)**beta     0 <= x <= 1, beta > 0

    with beta denoting the shape parameter.

    This distribution can be extended with lower and upper bound parameters. If a and b denote the lower and upper bounds, respectively, then the location and scale parameters are:

      location = a
      scale = b - a

    The general form of the distribution can then be found by using the relation

      F(x;beta,a,b) = F((x-a)/(b-a);beta,0,1)
Syntax:
    LET <y> = TOPCDF(<x>,<beta>,<a>,<b>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <x> is a number, parameter, or variable containing values in the interval (a,b);
                <y> is a variable or a parameter (depending on what <x> is) where the computed Topp and Leone cdf value is stored;
                <beta> is a positive number, parameter, or variable that specifies the shape parameter;
                <a> is a number, parameter, or variable that specifies the lower limit;
                <b> is a number, parameter, or variable that specifies the upper limit;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    If a and b are omitted, they default to 0 and 1, respectively.

Examples:
    LET A = TOPCDF(0.3,0.2)
    LET Y = TOPCDF(X,0.5,0,5)
    PLOT TOPCDF(X,2,0,3) FOR X = 0 0.01 3
Default:
    None
Synonyms:
    None
Related Commands:
    TOPPDF = Compute the Topp and Leone probability density function.
    TOPPPF = Compute the Topp and Leone percent point function.
    RGTPDF = Compute the generalized reflected Topp and Leone probability density function.
    GTLPDF = Compute the generalized Topp and Leone probability density function.
    TSPPDF = Compute the two-sided power probability density function.
    BETPDF = Compute the beta probability density function.
    TRIPDF = Compute the triangular probability density function.
    TRAPDF = Compute the trapezoid probability density function.
    UNIPDF = Compute the uniform probability density function.
    POWPDF = Compute the power probability density function.
    JSBPDF = Compute the Johnson SB probability density function.
Reference:
    Samuel Kotz and J. Rene Van Dorp 2004, "Beyond Beta: Other Continuous Families of Distributions with Bounded Support and Applications", World Scientific, chapter 2.
Applications:
    Distributional Modeling
Implementation Date:
    2007/2
Program 1:
     
    LABEL CASE ASIS
    TITLE CASE ASIS
    TITLE OFFSET 2
    .
    MULTIPLOT 2 2
    MULTIPLOT CORNER COORDINATES 0 0 100 95
    MULTIPLOT SCALE FACTOR
    .
    LET BETA  = 0.5
    TITLE Beta = ^beta
    PLOT TOPCDF(X,BETA) FOR X = 0  0.01  1
    .
    LET BETA  = 1
    TITLE Beta = ^beta
    PLOT TOPCDF(X,BETA) FOR X = 0  0.01  1
    .
    LET BETA  = 1.5
    TITLE Beta = ^beta
    PLOT TOPCDF(X,BETA) FOR X = 0  0.01  1
    .
    LET BETA  = 2
    TITLE Beta = ^beta
    PLOT TOPCDF(X,BETA) FOR X = 0  0.01  1
    .
    END OF MULTIPLOT
    .
    JUSTIFICATION CENTER
    MOVE 50 97
    TEXT TOPP AND LEONE CDF FUNCTIONS
        
    plot generated by sample program

Date created: 9/10/2007
Last updated: 9/10/2007
Please email comments on this WWW page to alan.heckert@nist.gov.