Message-ID: <50A690A8.7030907@yahoo.fr>
Date: 2012-11-16T19:14:48Z
From: Marc Girondot
Subject: fitting
In-Reply-To: <50A61A2F.6020809@icrm.cnr.it>
Le 16/11/12 11:49, Meli Massimiliano a ?crit :
> Hello All,
>
> i would fit my data with a function like this :
>
> y = a0 + a1 * exp(-x/a2) + a3 * exp(-x/a4) + a5 * exp(-x/a6) + a7 *
> exp(-x/a8) + a9 * exp(-x/a10)
>
> plus i have to impose that
>
> a1 + a3 + a5 + a7 + a9 = 1
>
> a1 , a3 , a5 , a7 , a9 >= 0
>
Then I conclude that 0<=a1, a3, a5, a7, a9<=1 and a1 + a3 + a5 + a7 +
a9 = 1.
To ensure that a1 + a3 + a5 + a7 + a9 = 1, your need to fit a1, a3, a5
and a7 but for a9, just impose a9=1-(a1+ a3+ a5+ a7).
To ensure 0<=a1 <=1, it is simpler to fit b1 as a real and to use it as
a1=1/(1+exp(b1))
Then a1 will be always as 0<=a1 <=1
(to be exact, it is 0<a1 <1 rather. Often it is sufficient)
Hope it help
--
__________________________________________________________
Marc Girondot, Pr
Laboratoire Ecologie, Syst?matique et Evolution
Equipe de Conservation des Populations et des Communaut?s
CNRS, AgroParisTech et Universit? Paris-Sud 11 , UMR 8079
B?timent 362
91405 Orsay Cedex, France
Tel: 33 1 (0)1.69.15.72.30 Fax: 33 1 (0)1.69.15.73.53
e-mail: marc.girondot at u-psud.fr
Web: http://www.ese.u-psud.fr/epc/conservation/Marc.html
Skype: girondot