## [SOLVED] How are defined the Hermite polynomials ?

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### [SOLVED] How are defined the Hermite polynomials ?

Hi,

I am trying to compute the conventional benefit with RGeostats.

For that, I carry out an anamorphosis of my data and build a program that uses the development of the conventional benefit on the Hermit polynomials as done in the non-linear lesson of Jacques Rivoirard (cours C-139, pp.49-50, 1991). In this lesson, he uses the Rodrigues formulation of the Hermit polynomials that introduces a normalization term.

Is it this formulation used in Rgeostats and if not, is the value of the field psi (coefficients of the anamorphosis) normalized by the factorial of the index i in the sum or not ?

Thanks for your help !

Maxime
Maxime Beauchamp

Posts: 29
Joined: Thu Jan 17, 2013 2:48 pm

### Re: How are defined the Hermit polynomials in RGeostats ?

Hi Maxime,

The Hermite polynomials are normalized in order that their variance is equal to 1 as it can be seen by computing the first 3 polynomials for the value 1

Code: Select all
`polynomial.eval(1,2)`

Moreover, you can now compute directly the conventional benefit from an anamorphosis object by using the RGeostats function

Code: Select all
`selectivity`

I hope it helped you.
Regards,
Nicolas
Nicolas Desassis

Posts: 196
Joined: Thu Sep 20, 2012 4:22 pm

### Re: How are defined the Hermit polynomials in RGeostats ?

Hi Nicolas,

For sure it will help.Thank you again.

It seems that the selectivity function enables to compute the conventional benefit for a defined dataset but is it possible to estimate the conventional benefit by disjunctive kriging or do I have to implement the method described in Rivoirard,1991 ?

Thanks a lot

Maxime
Maxime Beauchamp

Posts: 29
Joined: Thu Jan 17, 2013 2:48 pm

### Re: How are defined the Hermite polynomials in RGeostats ?

Hi,

I am going further than my previous post: if I effectively want to estimate the conventional benefit by disjunctive kriging, I will need the coefficients of the anamorphosis.

In my previous version of RGeostats, I have access to these coefficients via the slot psi of the object returned by anam.fit but it does no longer exist in the last version of the library. Has it been replaced by the slot hermite ? If not, is there a way to recover the coeffcients ?

Thanks again for the help !

Maxime
Maxime Beauchamp

Posts: 29
Joined: Thu Jan 17, 2013 2:48 pm

### Re: How are defined the Hermite polynomials in RGeostats ?

Hi Maxime,

according to the documentation, you should manage to access to the coefficients by the command

Code: Select all
`anam\$hermite`

where
Code: Select all
`anam`
is the object returned by
Code: Select all
`anam.fit`

Otherwise, the Disjunctive Kriging is not implemented yet in RGeostats.
You have to do it by yourself.

It should be implemented soon.
Regards,

Nicolas
Nicolas Desassis

Posts: 196
Joined: Thu Sep 20, 2012 4:22 pm

### Re: How are defined the Hermite polynomials in RGeostats ?

Okay,

Thanks for the quick answer ! I will so try to implement the disjunctive kriging by myself for the moment.

Maxime
Maxime Beauchamp

Posts: 29
Joined: Thu Jan 17, 2013 2:48 pm