JSUPDF

JSUPDF (LET)

Library Function

Compute the Johnson SU probability density function with shape parameters and .

The Johnson SU distribution has the following probability density function:



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

LET <y> = JSUPDF(<x>,<alpha1>,<alpha2>)             <SUBSET/EXCEPT/FOR qualification>
where <x> is a number, parameter, or variable;
            <y> is a variable or a parameter (depending on what <x> is) where the computed Johnson SU 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.

LET A = JSUPDF(2,0.3,2)
LET A = JSUPDF(A1,1.5,3)
LET Y = JSUPDF(X,2,6)
PLOT JSUPDF(X,0.8,2) FOR X = -5 0.1 20

None

None

JSUCDF	= Compute the Johnson SU cumulative distribution function.
JSUPPF	= Compute the Johnson SU percent point function.
JSBPDF	= Compute the Johnson SB 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.

"Continuous Univariate Distributions: Volume 1", 2nd. Ed., Johnson, Kotz, and Balakrishnan, Wiley, 1994, pp. 33-39.

Distributional Modeling

2001/11

    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 JSUPDF(X,A1,A2) FOR X = -10  0.1  10 
    END OF LOOP 
    END OF MULTIPLOT 
    .
    MOVE 50 97
    JUSTIFICATION CENTER
    HEIGHT 3
    TEXT JOHNSON SU PROBABILITY DENSITY FUNCTIONS