Dataplot Vol 2 Vol 1

# JSBCDF

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

where is the cumulative distribution function of the standard normal distribution and and 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
```

Date created: 11/20/2001
Last updated: 4/4/2003