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Dataplot Vol 2 Vol 1

RGTPPF

Name:
    RGTPPF (LET)
Type:
    Library Function
Purpose:
    Compute the reflected generalized Topp and Leone percent point function with shape parameters alpha and beta.
Description:
    The standard reflected generalized Topp and Leone distribution has the following percent point function:

      G(p;alpha,beta) = 
1-{alpha-SQRT(alpha**2-4*(alpha-1)*(1-p)**(1/beta)}/
{2*(alpha-1)}            for 1 < alpha <= 2       
1 - (1-p)**(1/beta)      for alpha = 1            
1-{alpha+SQRT(alpha**2-4*(alpha-1)*(1-p)**(1/beta)}/     
{2*(alpha-1)}            for 0 <= alpha < 1       
0 <= p <= 1, beta > 0

    with alpha and beta denoting the shape parameters.

    The standard distribution can be generalized with lower and upper bound parameters, a and b, respectively, by utilizing the following relation:

      G(p;alpha,beta,a,b) = a + (b-a)*G(p;alpha,beta,0,1)

    The lower and upper limits are related to the location and scale parameters as follows:

      location = a
      scale = b - a
Syntax:
    LET <y> = RGTPDF(<p>,<alpha>,<beta>,<a>,<b>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <p> is a number, parameter, or variable containing values in the interval (0,1);
                <y> is a variable or a parameter (depending on what <p> is) where the computed reflected generalized Topp and Leone ppf value is stored;
                <alpha> is a number, parameter, or variable in the interval (0, 2) that specifies the first shape parameter;
                <beta> is a positive number, parameter, or variable that specifies the second 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 = RGTPPF(0.95,0.2,1.2)
    LET Y = RGTPPF(P,0.5,2)
    PLOT RGTPPF(P,2,3) FOR P = 0 0.01 1
Default:
    None
Synonyms:
    None
Related Commands:
    RGTCDF = Compute the reflected generalized Topp and Leone cumulative distribution function.
    RGTPDF = Compute the reflected generalized Topp and Leone probability density function.
    GTLPDF = Compute the generalized Topp and Leone probability density function.
    TOPPDF = Compute the 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 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 7.
Applications:
    Distributional Modeling
Implementation Date:
    2007/2
Program:
     
    LABEL CASE ASIS
    TITLE CASE ASIS
    TITLE OFFSET 2
    .
    MULTIPLOT 3 3
    MULTIPLOT CORNER COORDINATES 0 0 100 95
    MULTIPLOT SCALE FACTOR 3
    .
    LET ALPHA = 2
    LET BETA  = 3
    TITLE Alpha = ^alpha, Beta = ^beta
    PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0  0.01  1
    .
    LET ALPHA = 1.5
    LET BETA  = 6
    TITLE Alpha = ^alpha, Beta = ^beta
    PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0  0.01  1
    .
    LET ALPHA = 1.5
    LET BETA  = 2
    TITLE Alpha = ^alpha, Beta = ^beta
    PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0  0.01  1
    .
    LET ALPHA = 1.5
    LET BETA  = 1
    TITLE Alpha = ^alpha, Beta = ^beta
    PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0  0.01  1
    .
    LET ALPHA = 0.5
    LET BETA  = 2
    TITLE Alpha = ^alpha, Beta = ^beta
    PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0  0.01  1
    .
    LET ALPHA = 0.5
    LET BETA  = 1
    TITLE Alpha = ^alpha, Beta = ^beta
    PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0  0.01  1
    .
    LET ALPHA = 0.5
    LET BETA  = 0.75
    TITLE Alpha = ^alpha, Beta = ^beta
    PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0  0.01  1
    .
    LET ALPHA = 0.5
    LET BETA  = 0.25
    TITLE Alpha = ^alpha, Beta = ^beta
    PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0  0.01  1
    .
    LET ALPHA = 1
    LET BETA  = 1
    TITLE Alpha = ^alpha, Beta = ^beta
    PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0  0.01  1
    .
    END OF MULTIPLOT
    .
    JUSTIFICATION CENTER
    MOVE 50 97
    TEXT Reflected Generalized Topp and Leone PPF Functions
        
    plot generated by sample program

Date created: 9/18/2007
Last updated: 9/18/2007
Please email comments on this WWW page to alan.heckert@nist.gov.