SED navigation bar go to SED home page go to Dataplot home page go to NIST home page SED Home Page SED Staff SED Projects SED Products and Publications Search SED Pages
Dataplot Vol 2 Vol 1

LBECDF

Name:
    LBECDF (LET)
Type:
    Library Function
Purpose:
    Compute the log beta cumulative distribution function with shape parameters alpha, beta, c, and d.
Description:
    The log beta distribution has the following probability density function:

      LBECDF(x;alpha,beta,c,d) = BETCDF(z;alpha,beta)
   0 < c <= x <= d;  alpha, beta > 0

    with alpha and beta 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

      z = (LOG(x) - LOG(c)/(LOG(d) - LOG(c))

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

Syntax:
    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).

Examples:
    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
Default:
    None
Synonyms:
    None
Related Commands:
    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.
Reference:
    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.
Applications:
    Distributional Modeling
Implementation Date:
    2006/8
Program:
     
    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
    .
    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
    .
    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
    .
    justification center
    move 50 97
    text Log Beta Cumulative Distribution Functions
        
    plot generated by sample program

Date created: 8/23/2006
Last updated: 8/23/2006
Please email comments on this WWW page to alan.heckert@nist.gov.