SED navigation bar go to SED home page go to Dataplot home page go to NIST home page SED Home Page SED Staff SED Projects SED Products and Publications Search SED Pages
Dataplot Vol 2 Vol 1

JSBPDF

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

      f(x) = [alpha2/(X*(1-X)]*NORPDF(ALPHA1 + ALPHA2*LOG(X/(1-X))
       0 < x < 1; alpha2 > 0

    where NORPDF is the probability density function of the standard normal distribution and alpha1 and alpha2 are shape parameters.

Syntax:
    LET <y> = JSBPDF(<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 pdf 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 = JSBPDF(2,0.3,2)
    LET A = JSBPDF(A1,1.5,3)
    LET Y = JSBPDF(X,2,6)
    PLOT JSBPDF(X,0.8,2) FOR X = -5 0.1 20
Default:
    None
Synonyms:
    None
Related Commands:
    JSBCDF = Compute the Johnson SB cumulative distribution 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 JSBPDF(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 PROBABILITY DENSITY 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.