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

B11CDF

Name:
    B11CDF (LET)
Type:
    Library Function
Purpose:
    Compute the Burr type 11 cumulative distribution function with shape parameter r.
Description:
    The Burr type 11 distribution is typically defined in terms of its cumulative distribution function:

      F(x;r,a,b) = [(x-a)/(b-a) - (1/(2*PI))*SIN(2*PI*(x-a)/(b-a))]^r 0 < (x-l)/s < 1; r, s > 0

    with r, a, and b denoting the shape, lower bound, and upper bound parameters, respectively.

    The location and scale parameters can be defined in terms of the lower and upper bound parameters:

      location = a
      scale = b - a

    The case where a = 0 and b = 1 is referred to as the standard Burr type 11 distribution.

Syntax:
    LET <y> = B11CDF(<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 11 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 = B11CDF(0.3,0.2)
    LET Y = B11CDF(X,0.5,0,5)
    PLOT B11CDF(X,2,0,3) FOR X = 0.01 0.01 2.99
Default:
    None
Synonyms:
    BURR TYPE XI is a synonym for BURR TYPE 11.
Related Commands:
    B11PDF = Compute the Burr type 11 probability density function.
    B11PPF = Compute the Burr type 11 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.
    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 B11CDF(X,R) FOR X = 0.01  0.01  0.99
.
LET R  = 1
TITLE R = ^r
PLOT B11CDF(X,R) FOR X = 0.01  0.01  0.99
.
LET R  = 2
TITLE R = ^r
PLOT B11CDF(X,R) FOR X = 0.01  0.01  0.99
.
LET R  = 5
TITLE R = ^r
PLOT B11CDF(X,R) FOR X = 0.01  0.01  0.99
.
END OF MULTIPLOT
.
JUSTIFICATION CENTER
MOVE 50 97
TEXT Burr Type 11 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.