LBECDF

LBECDF (LET)

Library Function

Compute the log beta cumulative distribution function with shape parameters , , c, and d.

The log beta distribution has the following probability density function:

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, BETCDF denoting the beta cumulative distribution function, and where

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

LET <y> = LBECDF(<y>,<alpha>,<beta>,<c>,<d>,<loc>,<scale>)
                        <SUBSET/EXCEPT/FOR qualification>
where <x> is a number, parameter, or variable;
            <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 <x> is) where the computed log beta cdf 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 = LBECDF(2,6,6,1,3)
LET Y = LBECDF(X,ALPHA,BETA,C,D)
PLOT LBECDF(X,6,6,1,3) FOR X = 1.01 0.01 2.99

None

None

LBEPDF	= Compute the log beta probability density function.
LBEPPF	= Compute the log beta percent point 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
y1label Probability
x1label X
.
let c = 1
let d = 3
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multiplot corner coordinates 0 0 100 95
multiplot scale factor 2
multiplot 2 2
.
title Alpha = 3, Beta = 3
plot lbecdf(x,3,3,c,d) for x = 1.01  0.01  2.99
.
title Alpha = 5, Beta = 2
plot lbecdf(x,5,2,c,d) for x = 1.01  0.01  2.99
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title Alpha = 2, Beta = 5
plot lbecdf(x,2,5,c,d) for x = 1.01  0.01  2.99
.
title Alpha = 5, Beta = 1
plot lbecdf(x,5,1,c,d) for x = 1.01  0.01  2.99
.
end of multiplot
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justification center
move 50 97
text Log Beta Cumulative Distribution Functions