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Dataplot Vol 2 Vol 1

BU2PPF

Name:
    BU2PPF (LET)
Type:
    Library Function
Purpose:
    Compute the Burr type 2 percent point function with shape parameter r.
Description:
    The standard Burr type 2 distribution has the following percent point function:

      G(p;r) = -LOG((1/p)**(1/r) - 1) 0 < p < 1; r > 0

    with r denoting the shape parameter.

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

      G(p;r,loc,scale)
    Syntax:
      LET <y> = BU2PPF(<p>,<r>,<loc>,<scale>)
                              <SUBSET/EXCEPT/FOR qualification>
      where <p> is a number, parameter, or variable in the interval (0,1);
                  <y> is a variable or a parameter (depending on what <p> is) where the computed Burr type 2 ppf 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 = BU2PPF(0.95,2.2)
      LET Y = BU2PPF(P,2.5,0,5)
      PLOT BU2PPF(P,2,0,3) FOR P = 0.01 0.01 0.99
    Default:
      None
    Synonyms:
      BURR TYPE II is a synonym for BURR TYPE 2.
    Related Commands:
      BU2PDF = Compute the Burr type 2 probability density function.
      BU2CDF = Compute the Burr type 2 cumulative distribution 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.
      BU5PDF = 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 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 2
.
LET R  = 0.5
TITLE R = ^r
PLOT BU2PPF(P,R) FOR P = 0.01  0.01  0.99
.
LET R  = 1
TITLE R = ^r
PLOT BU2PPF(P,R) FOR P = 0.01  0.01  0.99
.
LET R  = 2
TITLE R = ^r
PLOT BU2PPF(P,R) FOR P = 0.01  0.01  0.99
.
LET R  = 5
TITLE R = ^r
PLOT BU2PPF(P,R) FOR P = 0.01  0.01  0.99
.
END OF MULTIPLOT
.
JUSTIFICATION CENTER
MOVE 50 97
TEXT Burr Type 2 Percent Point Functions
      plot generated by sample program

    Date created: 11/27/2007
    Last updated: 11/27/2007
    Please email comments on this WWW page to [email protected].