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Dataplot Vol 2 Vol 1

JSBCDF

Name:
    JSBCDF (LET)
Type:
    Library Function
Purpose:
    Compute the Johnson SB cumulative distribution function with shape parameters alpha1 and alpha2.
Description:
    The Johnson SB distribution has the following cumulative distribution function:

      F(x) = NORCDF(ALPHA1 + ALPHA2*LOG(X/(1-X))
 0 < x < 1; alpha2 > 0

    where NORCDF is the cumulative distribution function of the standard normal distribution and alpha1 and alpha2 are shape parameters.

Syntax:
    LET <y> = JSBCDF(<x>,<alpha1>,<alpha2>)             <SUBSET/EXCEPT/FOR qualification>
    where <x> is a number, parameter, or variable containing values between 0 and 1;
                <y> is a variable or a parameter (depending on what <x> is) where the computed Johnson SB cdf values are stored;
                <alpha1> is a number, parameter, or variable that specifies the first shape parameter;
                <alpha2> is a number, parameter, or variable that specifies the second shape parameter;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = JSBCDF(2,0.3,2)
    LET A = JSBCDF(A1,1.5,3)
    LET Y = JSBCDF(X,2,6)
    PLOT JSBCDF(X,0.8,2) FOR X = -5 0.1 20
Default:
    None
Synonyms:
    None
Related Commands:
    JSBPDF = Compute the Johnson SB probability density function.
    JSBPPF = Compute the Johnson SB percent point function.
    JSUPDF = Compute the Johnson SU probability density function.
    BETPDF = Compute the beta probability density function.
    NORPDF = Compute the normal probability density function.
    UNIPDF = Compute the uniform probability density function.
    LAMPDF = Compute the Tukey-Lambda probability density function.
Reference:
    "Continuous Univariate Distributions: Volume 1", 2nd. Ed., Johnson, Kotz, and Balakrishnan, Wiley, 1994, pp. 33-39.
Applications:
    Distributional Modeling
Implementation Date:
    2001/11
Program:
        LET ALPHA1 = DATA 0.5 0.5 0.5 1 1 1 2 2 2 
        LET ALPHA2 = DATA 0.5 1 2 0.5 1 2 0.5 1 2 
        . 
        MULTIPLOT 3 3 
        MULTIPLOT CORNER COORDINATES 0 0 100 95 
        LOOP FOR K = 1 1 9 
           LET A1 = ALPHA1(K) 
           LET A2 = ALPHA2(K) 
           X1LABEL ALPHA1 = ^A1, ALPHA2 = ^A2 
           PLOT JSBCDF(X,A1,A2) FOR X = 0.01  0.01  0.99
        END OF LOOP 
        END OF MULTIPLOT 
        .
        MOVE 50 97
        HEIGHT 3
        JUSTIFICATION CENTER
        TEXT JOHNSON SB CUMULATIVE DISTRIBUTION FUNCTIONS
        
    plot generated by sample program

Date created: 11/20/2001
Last updated: 4/4/2003
Please email comments on this WWW page to alan.heckert@nist.gov.