LBEPPF

LBEPPF (LET)

Library Function

Compute the log beta percent point function with shape parameters , , c, and d.

The log beta percent point function can be computed using the beta percent point function as follows:

with and denoting the shape parameters of the underlying beta distribution, c and d denoting the lower and upper limits of the log beta distribution, and BETPPF denoting the beta percent point function.

The log beta distribution can be generalized with location and scale parameters in the usual way.

LET <y> = LBEPDF(<p>,<alpha>,<beta>,<c>,<d>,<loc>,<scale>)
                        <SUBSET/EXCEPT/FOR qualification>
where <p> is a number, parameter, or variable in the interval (0,1);
            <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;
            <c> is a number, parameter, or variable that specifies the third shape parameter;
            <d> is a number, parameter, or variable that specifies the fourth shape parameter;
            <loc> is a number, parameter, or variable that specifies the optional location parameter;
            <scale> is a number, parameter, or variable that specifies the optional scale parameter;
            <y> is a variable or a parameter (depending on what <p> is) where the computed log beta ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

The location and scale parameters are optional (the default values are zero and one, respectively).

LET A = LBEPPF(0.95,6,6,1,3)
LET Y = LBEPPF(P,ALPHA,BETA,C,D)
PLOT LBEPPF(P,6,6,1,3) FOR P = 0.01 0.01 0.99

None

None

LBECDF	= Compute the log beta cumulative distribution function.
LBEPDF	= Compute the log beta probability density function.
BETPDF	= Compute the beta probability density function.
BNOPDF	= Compute the beta normal probability density function.
LGNPDF	= Compute the lognormal probability density function.

Nadarajah and Gupta (2004). "Applications of the Beta Distribution" in "Handbook of the Beta Distribution", Edited by Gupta and Nadarajah, Marcel-Dekker, pp. 100-102.

Distributional Modeling

2006/8

 
title displacement 2
y1label displacement 17
x1label displacement 12
case asis
title case asis
label case asis
x1label Probability
y1label X
.
let c = 1
let d = 3
.
multiplot corner coordinates 0 0 100 95
multiplot scale factor 2
multiplot 2 2
.
title Alpha = 3, Beta = 3
plot lbeppf(p,3,3,c,d) for p = 0.01  0.01  0.99
.
title Alpha = 5, Beta = 2
plot lbeppf(p,5,2,c,d) for p = 0.01  0.01  0.99
.
title Alpha = 2, Beta = 5
plot lbeppf(p,2,5,c,d) for p = 0.01  0.01  0.99
.
title Alpha = 5, Beta = 1
plot lbeppf(p,5,1,c,d) for p = 0.01  0.01  0.99
.
end of multiplot
.
justification center
move 50 97
text Log Beta Percent Point Functions