Re: Finding unknown parameters using Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg74747] Re: Finding unknown parameters using Mathematica
- From: dh <dh at metrohm.ch>
- Date: Tue, 3 Apr 2007 00:31:00 -0400 (EDT)
- References: <euqnl6$894$1@smc.vnet.net>
Hi Shafiq.
there is something wrong in your code. What should:"=E2=88=91" mean? I
think "Sum". Note that it is better if you change your code to InputForm
before posting it. This is done by selecting and then menu: Cell/Convert
To/InputForm.
Further, your set up of the equations is wrong. What you wrote is:
Short Form of drivative == explicite Form of derivative
(D[L,r1]==...), what shlould give True. Note that the form: D[L,r1] is
only used in differential equations. In your case you would write:
eqns={ explicite form of derivative == 0, ...}
Solve[eqns,vars]
Daniel
Shafiq Ahmad wrote:
> Dear group members,
>
> I'm very new to mathematica and trying to solve a set of non-linear system =
> of equations to find the unknown parameters for a bivariate distribution. =
> I've 5 unknown parameters (i.e. b1,b2,r1,r2,p) and 5 set of equations. I =
> tried to get the general solution , but could not. I don't know how to =
> solve these nonlinear equations to get the unknown parameters. And also =
> not aware how to give initial value in the solve function or any other =
> function (e.g all parameters b1,b2,r1,r2,p if I give initial boundary =
> value =1).
> In the below codes, x1 and x2 are 2 variables (e.g. data from 2 quality =
> characteristics; stress and strain etc. etc.)
>
> Any comments / suggestions how to solve these equation for b1,b2,r1,r2,p =
> where as putting intial value for all these unknown parameters =1
>
> Ahmad S.
> ===================
> n=4
> x1={1,2,3,4}
> x2={1.7,3.8,4.9,4.6}
>
>
> 4
>
> {1,2,3,4}
>
> {1.7,3.8,4.9,4.6}
>
> \!\(\*
> RowBox[{
> RowBox[{
> StyleBox["L",
> FontSize->10],
> StyleBox["=",
> FontSize->14],
> StyleBox[\(n*Log[p] + n*Log[p + 1] + n*
> Log[b1] + n*Log[r1] + n*Log[b2] + n*Log[r2] + \((b1 - 1)\) =
> \(=E2=88=91\+\(j =
> 1\)\%n Log[x1[\([
> j]\)]]\) + \((b2 -
> 1)\) \(=E2=88=91\+\(j = 1\)\%n Log[
> x2[\([j]\)]]\) - \((p + 2)\) \(=E2=88=91\+\(j = 1\)\%n Log[1 +
> r1*\((x1[\([j]\)]^b1)\) + r2*\((x2[\([j]\)]^b2)\)]\)\),
> FontSize->14,
> FontColor->RGBColor[1, 0, 0]]}], "\[IndentingNewLine]",
> StyleBox[" ",
> FontSize->18]}]\)
>
> \!\(4.980920826406141`\ \((\(-1\) + b2)\) + \((\(-1\) + b1)\)\ \((
> Log[2] + Log[3] + Log[
> 4])\) + 4\ Log[b1] + 4\ Log[b2] + 4\ Log[
> p] + 4\ Log[1 + p] + 4\ Log[r1] + 4\ Log[r2] - \((2 + p)\)\ \((
> Log[1 + r1 + 1.7`\^b2\
> r2] + Log[1 + 2\^b1\ r1 + 3.8`\^b2\ r2] +
> Log[1 + 4\^b1\ r1 + 4.6`\^b2\ r2] + Log[1 + 3\^b1\ r1 + =
> 4.9`\^b2\
> r2])\)\)
>
> Eqn1=D[L,r1]\[Equal]0
>
>
> \!\(4\/r1 - \((2 +
> p)\)\ \((1\/\(1 + r1 + 1.7`\^b2\
> r2\) + 2\^b1\/\(1 + 2\^b1\ r1 + 3.8`\^b2\ r2\) + 4\^b1\/\(1 +
> 4\^b1\ r1 + 4.6`\^b2\ r2\) + 3\^b1\/\(1 + 3\^b1\ r1 + =
> 4.9`\^b2\ \
> r2\))\) \[Equal] 0\)
>
> Eqn2=D[L,r2]\[Equal]0
>
> \!\(4\/r2 - \((2 +
> p)\)\ \((1.7`\^b2\/\(1 +
> r1 + 1.7`\^b2\ r2\) + 3.8`\^b2\/\(1 + 2\^b1\ r1 + 3.8`\^b2\ r2\) =
> + \
> 4.6`\^b2\/\(1 +
> 4\^b1\ r1 + 4.6`\^b2\ r2\) + 4.9`\^b2\/\(1 + 3\^b1\ r1 + =
> 4.9`\^b2\
> \ r2\))\) \[Equal] 0\)
>
> Eqn3=D[L,b1]\[Equal]0
>
> \!\(4\/b1 + Log[2] + Log[3] + Log[4] - \((
> 2 + p)\)\ \((\(2\^b1\ r1\
> Log[2]\)\/\(1 + 2\^b1\ r1 + 3.8`\^b2\
> r2\) + \(3\^b1\ r1\ Log[3]\)\/\(1 + 3\^b1\ r1 + 4.9`\^b2\ r2\) + =
> \
> \(4\^b1\ r1\ Log[4]\)\/\(1 + 4\^b1\ r1 + 4.6`\^b2\ r2\))\) \[Equal] 0\)
>
> Eqn4=D[L,b2]\[Equal]0
>
>
> \!\(\(\(4.980920826406141`\)\(\[InvisibleSpace]\)\) +
> 4\/b2 - \((2 + p)\)\ \((\(0.5306282510621704`\ 1.7`\^b2\ r2\)\/\(1 =
> +
> r1 + 1.7`\^b2\
> r2\) + \(1.33500106673234`\ 3.8`\^b2\ r2\)\/\(1 + 2\^b1\ r1 + =
> \
> 3.8`\^b2\ r2\) + \(1.5260563034950492`\ 4.6`\^b2\ r2\)\/\(1 + 4\^b1\ r1 + =
> \
> 4.6`\^b2\ r2\) + \(1.589235205116581`\ 4.9`\^b2\ r2\)\/\(1 + 3\^b1\ r1 + =
> 4.9`\
> \^b2\ r2\))\) \[Equal] 0\)
>
> Eqn5=D[L,p]\[Equal]0
>
> \!\(4\/p + 4\/\(1 + p\) - Log[1 + r1 + 1.7`\^b2\
> r2] - Log[1 + 2\^b1\ r1 + 3.8`\^b2\ r2] - Log[1 + 4\^b1\
> r1 + 4.6`\^b2\ r2] - Log[1 + 3\^b1\ r1 + 4.9`\^b2\ r2] \[Equal] 0\)
>
> Solve[{Eqn1,Eqn2,Eqn3,Eqn4,Eqn5},{r1,r2,b1,b2,p}]
>