Dataplot Vol 2 Vol 1

# IBCDF

Name:
IBCDF (LET)
Type:
Library Function
Purpose:
Compute the standard inverted beta cumulative distribution function. This is also referred to as the beta distribution of the second kind or the beta prime distribution.
Description:
The standard inverted beta distribution has the following probability density function:

with B denoting the beta function (HELP BETA for details).

The inverted beta cumulative distribution function is computed by numerically integrating the inverted beta probability density function.

Syntax:
LET <y> = IBCDF(<x>,<alpha>,<beta>)
<SUBSET/EXCEPT/FOR qualification>
where <x> is a variable, a number, or a parameter;
<alpha> is a number or parameter specifying the first shape parameter;
<beta> is a number or parameter specifying the second shape parameter;
<y> is a variable or a parameter (depending on what <x> is) where the computed inverted beta cdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = IBCDF(3,2,1.5)
LET X2 = IBCDF(X1,A,B)
PLOT IBCDF(X,0.5,2) FOR X = 0.01 0.01 10
Note:
Dataplot uses the DQAGI routine from the Quadpack library to perform the numerical integration.
Default:
None
Synonyms:
None
Related Commands:
 IBPDF = Compute the inverted beta probability density function. IBPPF = Compute the inverted beta percent point function. BETPDF = Compute the beta probability density function. NORPDF = Compute the normal probability density function. RANDOM NUMBERS = Generate random numbers from 60+ univariate distributions.
Reference:
"Continuous Univariate Distributions, Volume 2", Second Edition, Johnson, Kotz, and Balakrishnan, Wiley, 1994, p. 248.

"Statistical Distributions", Third Edition, Evans, Hastings, and Peacock, Wiley, 2000.

Applications:
Distributional Modeling
Implementation Date:
2004/1
Program:
```
LET ALPHA = DATA 0.5 0.5 0.5 1 1 1 2 2 2
LET BETA = DATA 0.5 1 2 0.5 1 2 0.5 1 2
.
MULTIPLOT 3 3
MULTIPLOT CORNER COORDINATES 0 0 100 100
MULTIPLOT SCALE FACTOR 3
Y1LIMITS 0 1
MAJOR YTIC MARK NUMBER 6
LOOP FOR K = 1 1 9
LET A1 = ALPHA(K)
LET B1 = BETA(K)
TITLE ALPHA = ^A1, BETA = ^B1
PLOT IBCDF(X,A1,B1)  FOR X = 0.1  0.1 10
END OF LOOP
```

Date created: 2/3/2004
Last updated: 2/3/2004