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Dataplot Vol 2 Vol 1

GL2PPF

Name:
    GL2PPF (LET)
Type:
    Library Function
Purpose:
    Compute the type 2 generalized logistic percent point function with shape parameter alpha.
Description:
    The standard form of the type 2 generalized logistic distribution has the cumulative distribution function:

      F(x;alpha) = 1 - EXP(-alpha*x)/(1 + EXP(-x))**(alpha)   alpha > 0

    The generalized logistic type 2 percent point function is computed by numerically inverting the cumulative distribution function.

    The general form of the type 2 generalized logistic cumulative distribution function can be obtained by replacing x in the above formula with (x-loc)/scale.

Syntax:
    LET <y> = GL2PPF(<p>,<alpha>,<loc>,<scale>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <p> is a variable, number or parameter;
                <alpha> is a number or parameter that specifies the value of the shape parameter;
                <loc> is a number or parameter that specifies the value of the location parameter;
                <scale> is a number or parameter that specifies the value of the scale parameter;
                <y> is a variable or a parameter (depending on what <p> is) where the computed generalized logistic type 2 ppf value is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    The location and scale parameters are optional.

Examples:
    LET A = GL2PPF(0.95,2)
    LET X2 = GL2PPF(P1,ALPHA)
    PLOT GL2PPF(P,ALPHA) FOR P = 0.01 0.01 0.99
Default:
    None
Synonyms:
    None
Related Commands:
    GL2CDF = Compute the generalized logistic type 2 cumulative distribution function.
    GL2PDF = Compute the generalized logistic type 2 probability density function.
    GLOPDF = Compute the generalized logistic type 1 probability density function.
    GL3PDF = Compute the generalized logistic type 3 probability density function.
    GL4PDF = Compute the generalized logistic type 4 probability density function.
    GL5PDF = Compute the generalized logistic (Hosking parameterization) probability density function.
    LOGPDF = Compute the logistic probability density function.
    NORPDF = Compute the normal probability density function.
    LGNPDF = Compute the logmormal probability density function.
Reference:
    "Continuous Univariate Distributions - 2", 2nd. Ed., Johnson, Kotz, and Balakrishnan, John Wiley, 1994 (pp. 140-147).
Applications:
    Distributional Modeling
Implementation Date:
    2006/3
Program:
     
    LET A = DATA 0.5  1  2  5
    MULTIPLOT 2 2
    MULTIPLOT CORNER COORDINATES 0 0 100 95
    MULTIPLOT SCALE FACTOR 2
    LABEL CASE ASIS
    TITLE CASE ASIS
    TITLE DISPLACEMENT 2
    Y1LABEL X
    X1LABEL Probability
    X1LABEL DISPLACEMENT 12
    Y1LABEL DISPLACEMENT 15
    .
    LOOP FOR K = 1 1 4
       LET ALPHA = A(K)
       TITLE Alpha = ^ALPHA
       PLOT GL2PPF(P,ALPHA) FOR P = 0.01  0.01  0.99
    END OF LOOP
    END OF MULTIPLOT
    CASE ASIS
    MOVE 50 97
    JUSTIFICATION CENTER
    TEXT Generalized Logistic Type 2 PPF's
        
    plot generated by sample program

Date created: 3/27/2006
Last updated: 3/27/2006
Please email comments on this WWW page to alan.heckert@nist.gov.