IBPPF

IBPPF (LET)

Library Function

Compute the inverted beta cumulative distribution function. This is also referred to as the beta distribution of the second kind or the beta prime distribution.

The 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. The percent point function is computed by numerically inverting the cumulative distribution function.

LET <y> = IBPPF(<p>,<alpha>,<beta>)
                        <SUBSET/EXCEPT/FOR qualification>
where <p> is a variable, a number, or a parameter in the range [0,1];
            <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 <p> is) where the computed inverted beta ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET A = IBPPF(0.95,2,1.5)
LET X2 = IBPPF(P1,A,B)
PLOT IBPPF(P,0.5,2) FOR P = 0.01 0.01 0.99

None

None

IBCDF	= Compute the inverted beta cumulative distribution function.
IBPDF	= Compute the inverted beta probability density function.
BETPDF	= Compute the beta probability density function.
NORPDF	= Compute the normal 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

2004/1

 
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
.
XLIMITS 0 1
MAJOR XTIC MARK NUMBER 6
MINOR XTIC MARK NUMBER 1
.
MULTIPLOT 3 3
MULTIPLOT CORNER COORDINATES 0 0 100 100
MULTIPLOT SCALE FACTOR 3
LOOP FOR K = 1 1 9
    LET A = ALPHA(K)
    LET B = BETA(K)
    TITLE ALPHA = ^A, BETA = ^B
    PLOT IBPPF(P,^A,^B)  FOR P = 0.01 0.01 0.99
END OF LOOP
END OF MULTIPLOT