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}] >