IBCDF

IBCDF (LET)

Library Function

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.

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.

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.

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

Dataplot uses the DQAGI routine from the Quadpack library to perform the numerical integration.

None

None

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.

"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
.
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