JSBPPF

JSBPPF (LET)

Library Function

Compute the Johnson SB percent point 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.

The Johnson SB percent point function does not exist in simple closed form. It is computed numerically using a bisection method.

LET <y> = JSBPPF(<p>,<alpha1>,<alpha2>)             <SUBSET/EXCEPT/FOR qualification>
where <p> 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 ppf 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 = JSBPPF(0.95,0.5,2)
LET A = JSBPPF(P1,1.5,3)
LET Y = JSBPPF(P,2,6)
PLOT JSBPPF(P,0.8,2) FOR P = 0.01 0.01 0.99

None

None

JSBCDF	= Compute the Johnson SB cumulative distribution function.
JSBPDF	= Compute the Johnson SB probability density 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 JSBPPF(P,A1,A2) FOR P = 0.01  0.01  0.99 
    END OF LOOP 
    END OF MULTIPLOT 
    .
    MOVE 50 97
    HEIGHT 3
    JUSTIFICATION CENTER
    TEXT JOHNSON SB PERCENT POINT FUNCTIONS