BNOPPF

BNOPPF (LET)

Library Function

Compute the beta-normal percent point function with shape parameters and .

There are a class of distributions defined by the following cumulative distribution function:

with G(x) denoting a function. That is, this is the beta cumulative distribution function, but the upper limit of integration is defined by another cumulative distribution function.

The case where G(x) denotes the normal cumulative distribution function results in the beta-normal distribution with the following cumulative distribution function:

with denoting the cumulative distribution function of the standard normal distribution.

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

This distribution can be extended with location and scale parameters by replacing the standard normal distribution with a normal distribution with location parameter, , and scale parameter, . The and are also the location and scale parameter of the beta-normal distribution.

LET <y> = BNOPDF(<p>,<alpha>,<beta>,<loc>,<scale>)
                        <SUBSET/EXCEPT/FOR qualification>
where <p> is a number, parameter, or variable in the range [0,1];
            <y> is a variable or a parameter (depending on what <p> is) where the computed beta-normal ppf value is stored;
            <alpha> is a number, parameter, or variable that specifies the first shape parameter;
            <beta> is a number, parameter, or variable that specifies the second shape parameter;
            <loc> is a number, parameter, or variable that specifies the location parameter;
            <scale> is a number, parameter, or variable that specifies the scale parameter;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

The <loc> and <scale> parameters are optional.

LET A = BNOPPF(0.95,0.1,0.1)
LET X2 = BNOPPF(P1,0.1,0.1)
PLOT BNOPPF(P,0.1,0.1) FOR P = 0.01 0.01 0.99

None

None

BNOCDF	= Compute the beta-normal cumulative distribution function.
BNOPDF	= Compute the beta-normal probability density function.
BETPDF	= Compute the beta probability density function.
NORPDF	= Compute the normal probability density function.
GAMPDF	= Compute the gamma probability density function.

"Handbook of Beta Distribution and Its Applications", Edited by Arjun Gupta and Saralees Nadarajah, Marcel Dekker Inc., 2004, pp. 146-152.

Eugene, Lee, and Famoye (2002). "Beta-Normal Distribution and Its Applications", Communications in Statistics-Theory and Methods, 31, pp. 497-512.

Distributional Modeling

2006/3

MULTIPLOT 3 3
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 3
LABEL CASE ASIS
Y1LABEL X
X1LABEL Probability
X1LABEL DISPLACEMENT 14
Y1LABEL DISPLACEMENT 15
TITLE DISPLACEMENT 2
.
LET A = DATA 0.1  1  5
LET B = DATA 0.1  1  5
LOOP FOR K = 1 1 3
    LET ALPHA = A(K)
    LOOP FOR L = 1 1 3
        LET BETA = B(L)
        TITLE ALPHA = ^ALPHA, BETA = ^BETA
        PLOT BNOPPF(P,ALPHA,BETA) FOR P = 0.01  0.01  0.99
    END OF LOOP
END OF LOOP
.
END OF MULTIPLOT
JUSTIFICATION CENTER
MOVE 50 97
CASE ASIS
TEXT PPF's For Beta-Normal Distribution