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Dataplot Vol 2 Vol 1

BU3CDF

Name:
    BU3CDF (LET)
Type:
    Library Function
Purpose:
    Compute the Burr type 3 cumulative distribution function with shape parameters r and k.
Description:
    The Burr type 3 distribution is typically defined in terms of its cumulative distribution function:

      F(x;r,k,l,s) = (1+((x-l)/s)**(-k))**(-r)      x >  0; r, k > 0

    with r, k, l, and s denoting the two shape parameters, the location parameter, and the scale parameter, respectively.

    The case where l = 0 and s = 1 is referred to as the standard Burr type 3 distribution.

    If X has a Burr type 12 distribution, then 1/X has a Burr type 3 distribution. For this reason, the Burr type 3 distribution is often referred to as the inverse Burr distribution.

    The Burr type 3 distribution is also sometimes referred to as the Dagum type I distribution.

Syntax:
    LET <y> = BU3CDF(<x>,<r>,<k>,<loc>,<scale>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <x> is a number, parameter, or variable;
                <y> is a variable or a parameter (depending on what <x> is) where the computed Burr type 3 cdf value is stored;
                <r> is a positive number, parameter, or variable that specifies the first shape parameter;
                <k> is a positive 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 positive number, parameter, or variable that specifies the scale parameter;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    If <loc> and <scale> are omitted, they default to 0 and 1, respectively.

Examples:
    LET A = BU3CDF(0.3,0.2,1.7)
    LET Y = BU3CDF(X,0.5,2,2,0,5)
    PLOT BU3CDF(X,2,0,3) FOR X = 0 0.01 5
Default:
    None
Synonyms:
    BURR TYPE III is a synonym for BURR TYPE 3.
Related Commands:
    BU3PDF = Compute the Burr type 3 probability density function.
    BU3PPF = Compute the Burr type 3 percent point function.
    BU2PDF = Compute the Burr type 2 probability density function.
    BU3PDF = Compute the Burr type 3 probability density function.
    BU4PDF = Compute the Burr type 4 probability density function.
    BU5PDF = Compute the Burr type 5 probability density function.
    BU6PDF = Compute the Burr type 6 probability density function.
    BU7PDF = Compute the Burr type 7 probability density function.
    BU8PDF = Compute the Burr type 8 probability density function.
    BU9PDF = Compute the Burr type 9 probability density function.
    B10PDF = Compute the Burr type 10 probability density function.
    B11PDF = Compute the Burr type 11 probability density function.
    B12PDF = Compute the Burr type 12 probability density function.
    RAYPDF = Compute the Rayleigh probability density function.
    WEIPDF = Compute the Weibull probability density function.
    EWEPDF = Compute the exponentiated Weibull probability density function.
Reference:
    Burr (1942), "Cumulative Frequency Functions", Annals of Mathematical Statistics, 13, pp. 215-232.

    Johnson, Kotz, and Balakrishnan (1994), "Contiunuous Univariate Distributions--Volume 1", Second Edition, Wiley, pp. 53-54.

    Devroye (1986), "Non-Uniform Random Variate Generation", Springer-Verlang, pp. 476-477.

Applications:
    Distributional Modeling
Implementation Date:
    2007/10
Program:
     
    LABEL CASE ASIS
    TITLE CASE ASIS
    TITLE OFFSET 2
    .
    MULTIPLOT 4 4
    MULTIPLOT CORNER COORDINATES 0 0 100 95
    MULTIPLOT SCALE FACTOR 4
    .
    LET RVAL = DATA 0.5  1  2  5
    LET KVAL = DATA 0.5  1  2  5
    .
    LOOP FOR IROW = 1 1 4
        LOOP FOR ICOL = 1 1 4
            LET R  = RVAL(IROW)
            LET K = KVAL(ICOL)
            TITLE R = ^r, K = ^k
            PLOT BU3CDF(X,R,K) FOR X = 0.01  0.01  5
        END OF LOOP
    END OF LOOP
    .
    END OF MULTIPLOT
    .
    JUSTIFICATION CENTER
    MOVE 50 97
    TEXT Burr Type 3 Cumulative Distribution Functions
        
    plot generated by sample program

Date created: 11/27/2007
Last updated: 11/27/2007
Please email comments on this WWW page to alan.heckert@nist.gov.