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Dataplot Vol 2 Vol 1

B12CDF

Name:
    B12CDF (LET)
Type:
    Library Function
Purpose:
    Compute the Burr type 12 cumulative distribution function with shape parameters c and k.
Description:
    The Burr type 12 distribution is typically defined in terms of its cuumulative distribution function:

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

    with c, 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 12 distribution.

    The Burr type 12 distribution is also sometimes referred to as the Singh-Maddala distribution.

Syntax:
    LET <y> = B12CDF(<x>,<c>,<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 12 cdf value is stored;
                <c> 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 = B12CDF(0.3,0.2,1.7)
    LET Y = B12CDF(X,0.5,2,2,0,5)
    PLOT B12CDF(X,2,0,3) FOR X = 0 0.01 5
Default:
    None
Synonyms:
    BURR TYPE XII is a synonym for BURR TYPE 12.
Related Commands:
    B12PDF = Compute the Burr type 12 probability density function.
    B12PPF = Compute the Burr type 12 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.
    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 CVAL = 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 C  = CVAL(IROW)
            LET K = KVAL(ICOL)
            TITLE C = ^c, K = ^k
            PLOT B12CDF(X,C,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 12 Cumulative Distribution Functions
        
    plot generated by sample program

Date created: 12/17/2007
Last updated: 12/17/2007
Please email comments on this WWW page to alan.heckert@nist.gov.