IBPDF

IBPDF (LET)

Library Function

Compute the inverted beta probability density function. This is also referred to a beta distribution of the second kind or a beta prime distribution.

The inverted beta distribution has the following probability density function:

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

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.

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

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

None

None

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.

"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.

Distributional Modeling

2003/5

 
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