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MathGroup Archive 2006

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Re: NonLinearRegress Problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68366] Re: NonLinearRegress Problem
  • From: Peter Pein <petsie at dordos.net>
  • Date: Thu, 3 Aug 2006 06:06:22 -0400 (EDT)
  • References: <eapr5l$s0h$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

jour schrieb:
> I have the following problem with NonLinearRegress
> 
> I have defined the following function
> 
> deb[teta_,n_,t]:= 9 n (t/teta)^3 Nintegrate[(x^4
> Exp[x])/(1+Exp[x])^2,{x,0,t/teta}]
> 
> I can Table this function without problem
> 
> Table[{t, deb2[100, 3, t]}, {t, 1, 200, 5}]
> 
> but when I try to use this function in NonlinearRegress
> 
> fut = NonlinearRegress[dat,
> deb2[teta, n, t],
> {t}, {{teta, {10., 50.}, 0., 1000.}, {n, {1, 3}, 1, 70}}]
> 
> I get an error message
> 
> NIntegrate::"nlim"  t/teta is not a valid limit of integration
> 
> any suggestions ?
> 
bon(jour)^2

1.) what is deb2?
2. & 3.) deb[teta_,n_,t_]:=...NIntegrate[...]
                       ^^^     ^^^
4.) either use
(*I recommend this *)
deb2[teta_,n_,t_]= 9 n (t/teta)^3 *Integrate[(x^4 Exp[x])/(1+Exp[x])^2,{x,0,t/teta}]

   or

ndeb2[teta_,n_,t_]:= 9 n (t/teta)^3 *NIntegrate[(x^4 Exp[x])/(1+Exp[x])^2,{x,0,t/teta}]/;And@@(NumericQ/@{teta,n,t})


When naming the table from your posting dat, the ndeb2 version needs 13 seconds on my computer to complete

fut = NonlinearRegress[dat, deb2[teta, n, t], {t},
  {{teta, {10, 300}, 0, 1000}, {n, {1, 8}, 1, 70}}]

and the exact version needs ~178 seconds.

*But* NonlinearRegress can't find the derivatives of the model ndeb2 and therefore calculates only BestFitParameters, EstimatedVariance and ANOVATable.

Peter


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