Dataplot Vol 2 Vol 1

IBPDF

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

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

Syntax:
LET <y> = IBPDF(<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 pdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = IBPDF(3,2,1.5)
LET X2 = IBPDF(X1,A,B)
PLOT IBPDF(X,0.5,2) FOR X = 0.01 0.01 10
Note:
Currently the cumulative distribution function and percent point function are not implemented in Dataplot. We plan to add these at a later date.

You can generate random numbers from an inverted beta distribution with the following command:

LET ALPHA = <value>
LET BETA = <value>
LET Y = INVERTED BETA RANDOM NUMBERS FOR I = 1 1 N
Default:
None
Synonyms:
None
Related Commands:
 IBCDF = Compute the inverted beta cumulative distribution function. IBPPF = Compute the inverted beta percent point function. NORPDF = Compute the normal probability density function. LOGPDF = Compute the logistic probability density function. CAUPDF = Compute the Cauchy 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:
2003/5
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
LOOP FOR K = 1 1 9
LET A1 = ALPHA(K)
LET B1 = BETA(K)
TITLE ALPHA = ^A1, BETA = ^B1
PLOT IBPDF(X,A1,B1)  FOR X = 0.01  0.01 10
END OF LOOP
```

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