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Dataplot Vol 2 Vol 1

BU8CDF

Name:
    BU8CDF (LET)
Type:
    Library Function
Purpose:
    Compute the Burr type 8 cumulative distribution function with shape parameter r.
Description:
    The Burr type 8 distribution is typically defined in terms of its cumulative distribution function:

      F(x;r,l,s) = ((2/PI)*ARCTAN(EXP((x-l)/s)))^r -INF < x < INF; r, s > 0

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

    The case where l = 0 and s = 1 is referred to as the standard Burr type 8 distribution.

Syntax:
    LET <y> = BU8CDF(<x>,<r>,<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 8 cdf value is stored;
                <r> is a positive number, parameter, or variable that specifies the 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 = BU8CDF(0.3,0.2)
    LET Y = BU8CDF(X,0.5,0,5)
    PLOT BU8CDF(X,2,0,3) FOR X = -3 0.01 3
Default:
    None
Synonyms:
    BURR TYPE VIII is a synonym for BURR TYPE 8.
Related Commands:
    BU8PDF = Compute the Burr type 8 probability density function.
    BU8PPF = Compute the Burr type 8 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.
    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 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 2
.
LET R  = 0.5
TITLE R = ^r
PLOT BU8CDF(X,R) FOR X = -3  0.01  3
.
LET R  = 1
TITLE R = ^r
PLOT BU8CDF(X,R) FOR X = -3  0.01  3
.
LET R  = 2
TITLE R = ^r
PLOT BU8CDF(X,R) FOR X = -3  0.01  3
.
LET R  = 5
TITLE R = ^r
PLOT BU8CDF(X,R) FOR X = -3  0.01  3
.
END OF MULTIPLOT
.
JUSTIFICATION CENTER
MOVE 50 97
TEXT Burr Type 8 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.