Re: DATAPLOT question

[N Alan Heckert <alan.heckert@nist.gov>]

On Fri, 2007-10-12 at 17:01 -0600, Chris Peltz wrote:

Chris,

 1. Dataplot supports the following distributions used in extreme value
    analysis:

    a. Extreme value type I (Gumbel)   - EV1PDF, etc.
    b. Extreme value type II (Frechet) - EV2PDF, etc.
    c. Generalized extreme value       - GEVPDF, etc.
    d. Weibull                         - WEIPDF, etc.
    e. Generalized Pareto              - GEPPDF, etc.

 2. Extreme value distributions can be based on either the
    minimum order statistic or the maximum order statistic.

    In Dataplot, this is specificed using the

        SET MINMAX <MIN/MAX>

    This is currently supported for all of the above distributions
    except the generalized Pareto (this will be added in a 
    future release).

    The default is MIN for Weibull and MAX for the others.

    This distinction is not always made clear in
    the literature (i.e., many sources will list the formulas
    for these distributions without specifying whether it is
    based on the minimum or maximum order statistic). 

    Reference is also made to "reverse Weibull" or "reverse Gumbel"
    or the "reverse Frechet".  These are simply the Weibull distribution
    based on the maximum order statistic and the Gumbel or
    Frechet based on the minimum order statistic.

 3. The extreme value type 3 is either the Weibull (for the minimum
    case) or reverse Weibull (for the maximum case).

    For example, Bury (Statistical Distributions in Engineering,
    Cambridge University Press) on page 311 equate the Weibull to
    the extreme value type III for minima.  Johnson, Kotz, and 
    Balakrishnan (Continuous Univariate Distributions, Volume 2,
    Second Edition, Wiley) equate the extreme value type 3 to
    the reverse Weibull without explicitly stating whether the
    minimum or maximum case is being considered (in this case,
    it is the maximum).

 4. So in Dataplot, you first need to know whether you need the
    minimum or maximum case for the extreme value type 3.  If the
    minimum case, just use the Weibull.  For the maximum case,
    enter SET MINMAX MAX and then use the Weibull.  Note that
    the MINMAX switch stays set until you change it (and also
    be aware that it applies to the EV1, EV2, and GEV
    distributions as well).


Alan
     
> The DATAPLOT software supports Type I and Type II extreme event
> distributions. What about Type III – is there a function available for
> that?
> 
>