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Dataplot Vol 2 Vol 1

BU9PPF

Name:
    BU9PPF (LET)
Type:
    Library Function
Purpose:
    Compute the Burr type 9 percent point function with shape parameters r and k.
Description:
    The standard Burr type 9 distribution has the following percent point function:

      G(p;r,k) = LOG{[1 + (1/k)*(2/(1-p) - 2)]**(1/r) - 1}     
0 < p < 1; r, k > 0

    with r and k denoting the shape parameters.

    This distribution can be generalized with location and scale parameters in the usual way using the relation

      G(p;r,k,loc,scale) = loc + scale*G(p;r,k,0,1)
Syntax:
    LET <y> = BU9PPF(<p>,<r>,<k>,<loc>,<scale>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <p> is a number, parameter, or variable;
                <y> is a variable or a parameter (depending on what <p> is) where the computed Burr type 9 ppf 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 = BU9PPF(0.95,0.2,1.7)
    LET Y = BU9PPF(P,0.5,2.2,0,5)
    PLOT BU9PPF(P,2,1.8) FOR X = 0.01 0.01 0.99
Default:
    None
Synonyms:
    BURR TYPE IX is a synonym for BURR TYPE 9.
Related Commands:
    BU9CDF = Compute the Burr type 9 cumulative distribution function.
    BU9PDF = Compute the Burr type 9 probability density 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.
    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 BU9PPF(P,R,K) FOR P = 0.01  0.01  0.99
        END OF LOOP
    END OF LOOP
    .
    END OF MULTIPLOT
    .
    JUSTIFICATION CENTER
    MOVE 50 97
        
    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.