Basically what you are suggesting is the use of class
indicators instead of cumulative indicators to
build the conditional cumulative distribution function
(ccdf) in a non-parametric way. Both approaches should
give similar results and have been compared by a few
authors; for example:
Benamghar and Sonnet. 1999. Performance comparison of
cumulative and class indicators approaches for pollution
risk assessment. In J.~G\'omez-Hern\'andez, A.~Soares, and
R.~Froidevaux, editors, geoENV II - Geostatistics for
Environmental Applications, pages 357-368.
Kluwer Academic Publishers, Dordrecht.
Wingle, W.L., and E.P. Poeter, 1998, Classes vs. Thresholds: A
Modification to Traditional Indicator Simulation, Advances in
Geostatistics, 1998 AAPG Annual Meeting, Salt Lake
City, Utah, May 17-20, 1998, which is available at
The only potential drawback with class indicators
is that the experimental semivariograms will tend to
be more erratic than for cumulative indicators because
they will be based on a smaller proportions of non-zero
data. For example, if you use decile thresholds to
define 10 classes, each class indicator variable will
consist of 10% of 1 and 90% of 0, while for cumulative
indicators this ratio will be observed only for the
first and last threshold. It's the reason why the
semivariogram for a median threshold (50% of 1 and 50%
of 0) is usually one of the best behaved.
| \ / | Pierre Goovaerts
|_ \ / _| Assistant professor
__|________\/________|__ Dept of Civil & Environmental Engineering
| | The University of Michigan
| M I C H I G A N | EWRE Building, Room 117
|________________________| Ann Arbor, Michigan, 48109-2125, U.S.A
_| |_\ /_| |_
| |\ /| | E-mail: goovaert@...
|________| \/ |________| Phone: (734) 936-0141
Fax: (734) 763-2275
On Wed, 27 Sep 2000, NEFIA NEFIA wrote:
> Dear list,
> Does anyone have any opinions on this technique:
> To use a non parametric approach to dealing with zero-heavy data (extremely
> skewed distribution), it was suggested to me to use a series of indicator
> variograms. I'm interested not in the probability of exceeding a given
> threshhold, but rather in the membership of each estimtate in one of a set
> of classes (say, deciles of a distribution).
> So why not indicator code each original datum (1,0) as to whether or not
> that datum falls in a given decile (not 1,0 based on whether it exceeds a
> threshhold, as is typically done with indicator kriging), then do 10
> indicator variograms, make 10 indicator kriged maps, and ask the question
> "which map has the highest value, i.e. the highest probability of membership
> within the decile corresponding to that map". The decile that "wins" for
> each pixel will be the decile that gets assigned as the final value for that
> So, my thought is that what I've done is made a map of "most probable class
> membership" and (perhaps) have dealt with the problem of having a highly
> skewed distribution in a non parametric way.
> Is this a common technique? It seems like it might be, but maybe I'm
> overlooking something.
> Thanks for any of your wisdom!
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