JSBPDF

JSBPDF (LET)

Library Function

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

The Johnson SB 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> = 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.

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

None

None

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.

"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 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