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MathGroup Archive 2007

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Re: Running a loop for Maximizing problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75477] Re: Running a loop for Maximizing problem
  • From: Daniel Huber <dh at metrohm.ch>
  • Date: Wed, 2 May 2007 03:53:22 -0400 (EDT)
  • References: <463878370200000B002AFE55@its-gw-inet57.its.rmit.edu.au>

Hi Shafiq,
OLE has 3 not 2 variables: b1,b2 and p. Do you want a maximum relative 
to all 3 variables or only relative to b1 and b2 with p kept constant? 
It seems that the variables must fullfill some restrictions, otherwise 
OLE is not even real. Further, does OLE really have a global maximum or 
are you looking for a local maximum?
Daniel

Shafiq Ahmad wrote:
> Hi 
>
> I've a non linear equation (OLE) and need to solve it to get the Maximum
> Likelihood values.  To do so, I tried a loop that every time the value
> of b1 and b2 changes ranging from 10 to 100 with step of 10 and  get the
> Maximized value for OLE.   The idea behind is to find a contour or
> surface with axis such as b1=X-axis, b2=Y-axis and OLE= Zaxis
>
> Is any one can suggest any idea? Below are the codes I tried
> ============================
>
> In[173]:=
> n = 20
> x1 = {1.04, 1.06, 1.09, 1.05, 1.07, 1.06, 1.05, 1.1, 1.09, 1.05, 0.99,
> 1.06, 1.05, 1.07, 1.11, 1.04, 1.03, 1.05, 1.06, 1.04}
> x2 = {115.25, 115.91, 115.05, 116.21, 115.9, 115.55, 114.98, 115.25,
> 116.15, 115.92, 115.75, 114.9, 116.01, 115.83, 115.29, 115.63, 115.47,
> 115.58, 115.72, 115.4}
>
> pars = {b1, b2}
> valsset = Table[{b1, b2}, {b1, 10, 100, 10}, {b2, 10, 100, 10}]
> valsset = Flatten[valsset, 1]
> rules = (MapThread[Rule, {pars, #1}] & ) /@ valsset
> L/.rules
>
> In[176]:=
> OLE = n*Log[p] + n*Log[p + 1] + n*Log[b1] + n*Log[b2] + (b1 -
> 1)*Sum[Log[x1[[j]]], {j, 1, n}] + (b2 - 1)*Sum[Log[x2[[j]]], {j, 1, n}]
> - 
>    (p + 2)*Sum[Log[1 + x1[[j]]^b1 + x2[[j]]^b2], {j, 1, n}]
>
> In[177]:=
> Eqn1 = D[OLE, b1] == 0
> Eqn2 = D[OLE, b2] == 0
> Eqn3 = D[OLE, p] == 0
> FindRoot[{Eqn1, Eqn2, Eqn3}, {b1, 10}, {b2, 10}, {p, 1}]
>
> ============================
>
>
>   


-- 

Daniel Huber
Metrohm Ltd.
Oberdorfstr. 68
CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh at metrohm.ch>
Internet:<http://www.metrohm.ch>



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