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 <b...@xs4all.nl>
>Subject: Re: [R] Solving two nonlinear equations with two knowns
>To: r-help@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.
>
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