[R] Solving two nonlinear equations with two knowns

[yhsu6 at illinois.edu]

Thanks a lot Berend and Ravi!!!
I am thinking to use integrate command to get theoretical E(X), E(Y), Var(X), and Var(Y). Then the result will not depend on u anymore. After that, I will use dfsane command in BB package.

Kate


---- Original message ----
>Date: Fri, 17 Jul 2009 09:51:34 -0700 (PDT)
>From: Berend Hasselman <bhh at xs4all.nl>  
>Subject: Re: [R] Solving two nonlinear equations with two knowns  
>To: r-help at r-project.org
>
>
>
>
>yhsu6 wrote:
>> 
>> 
>> ########## 
>> #R code: 
>> mu2=0.4 
>> sigma2=4 
>> tau=0.75 
>> mean.diff=2 
>> var.ratio=3 
>> 
>> #Use optim: 
>> parameter<-function(c) 
>> { 
>> a<-c[1] 
>> b<-c[2] 
>> u<-runif(10000) 
>> Y<-qnorm(u,mean=mu2,sd=sigma2) 
>> u<-runif(10000) 
>> X<-qnorm(u,mean=mu2,sd=sigma2)+a*abs(u-tau)^b*(u>tau) 
>> return((abs(mean(X)-mean(Y))-mean.diff)^2+(var(X)/var(Y)-var.ratio)^2) 
>> } 
>> 
>> 
>> c0<-c(3,1) 
>> cstar<-optim(c0,parameter)$par 
>> astar<-cstar[1] #4.1709 
>> bstar<-cstar[2] #-0.2578 
>> 
>> 
>
>Your problem is ill posed.
>In your function you have two u <- runif(10000) statements
>This means that every time your function is called, u changes.
>You can see this happening by repeating parameter(c0) several times
>
>parameter(c0)
>[1] 7.346233
>parameter(c0)
>[1] 7.204457
>
>So you are trying to optimise a function that gives different results for
>the same parameter vector every  time it is called. You can't determine a
>and b that way.
>This will never work.
>
>The two u<-runif(10000) should be removed from the function body and should
>be done only once before calling the function.
>Your function then becomes
>
>zparameter<-function(c) 
>{ 
>a<-c[1] 
>b<-c[2] 
>Y<-qnorm(u,mean=mu2,sd=sigma2) 
>X<-qnorm(u,mean=mu2,sd=sigma2)+a*abs(u-tau)^b*(u>tau) 
>z<-numeric(2)
>z[1] <- abs(mean(X)-mean(Y))-mean.diff
>z[2] <- var(X)/var(Y)-var.ratio
>z
>} 
>
>BTW: you can make this function more efficient by moving the expression for
>Y outside the function body and writing X<=Y+.....
>
>If you do this, you should get sensible results. For solving a system of
>equation I would not use optim.
>Use an equation solver (nleqslv or BB).
>
>Berend
>
>-- 
>View this message in context: http://www.nabble.com/Solving-two-nonlinear-equations-with-two-knowns-tp24528892p24538026.html
>Sent from the R help mailing list archive at Nabble.com.
>
>______________________________________________
>R-help at r-project.org mailing list
>https://stat.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>and provide commented, minimal, self-contained, reproducible code.