From: Paul Smith <phhs80_at_gmail.com>

Date: Fri, 25 Apr 2008 14:35:38 +0100

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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. Received on Fri 25 Apr 2008 - 13:47:44 GMT

Date: Fri, 25 Apr 2008 14:35:38 +0100

Clearly, a family of solutions is

(p,q) = (0,k), with k != 0.

Paul

On Fri, Apr 25, 2008 at 1:58 PM, Paul Smith <phhs80_at_gmail.com> wrote:

> Try to change the initial values of the parameters with, for instance,

*>
**> p0 <- rnorm(2)
**>
**> But you sure that your system has a solution, Evgeniq?
**>
**> Paul
**>
**>
**>
**>
**> 2008/4/25 Radka Pancheva <radica_at_abv.bg>:
**> > Hello Paul,
**> >
**> > Thank you for your quick answer. I have tried to use your advice and to estimate the parameters of beta distribution with moments matching. This is my code:
**> >
**> >
**> > ex <- 0.3914877
**> > ex2 <- 0.2671597
**> >
**> > my.mm <- function(x){
**> > p <- x[1]
**> > q <- x[2]
**> > p <- .Machine$double.eps
**> > q <- .Machine$double.eps
**> >
**> > F <- rep(NA,2)
**> >
**> > F[1] <- p/(p + q)
**> > F[2]<- (p*q + (p + q + 1)*p^2)/((p + q + 1)*(p + q)^2)
**> >
**> > return(F)
**> > }
**> >
**> > p0 <- c(ex,ex2)
**> >
**> > dfsane(par=p0, fn=my.mm,control=list(maxit=50000))
**> >
**> > and I became the following output:
**> >
**> > …
**> > iteration: 3640 ||F(xn)|| = 0.7071068
**> > iteration: 3641 ||F(xn)|| = 0. 7071068
**> > …
**> > iteration: 49990 ||F(xn)|| = 0. 7071068
**> > iteration: 50000 ||F(xn)|| = 0. 7071068
**> > $par
**> > [1] -446.2791 -446.4034
**> >
**> > $residual
**> > [1] 0.5
**> >
**> > $fn.reduction
**> > [1] 0
**> >
**> > $feval
**> > [1] 828495
**> >
**> > $iter
**> > [1] 50001
**> >
**> > $convergence
**> > [1] 1
**> >
**> > $message
**> > [1] "Maximum limit for iterations exceeded"
**> >
**> > I have tried maxiter=100000 but the output is the same. I know that ex and ex2 are bringing the problems, but I am stuck with them. How can I make it convergent?
**> >
**> > Thank you,
**> >
**> > Evgeniq
**> >
**> >
**> >
**> > >2008/4/25 Radka Pancheva <radica_at_abv.bg>:
**> > >> I am trying to estimate the parameters of a bimodal normal distribution using moments matching, so I have to solve a non-linear system of equations. How can I solve the following simple example?
**> > >>
**> > >> x^2 - y^2 = 6
**> > >> x – y = 3
**> > >>
**> > >> I heard about nlsystemfit, but I don't know how to run it exactly. I have tried the following code, but it doesn't really work:
**> > >>
**> > >>
**> > >> f1 <-y~ x[1]^2-x[2]^2-6
**> > >> f2 <-z~ x[1]-x[2]-3
**> > >> f <- list(f1=0,f2=0)
**> > >> nlsystemfit("OLS",f,startvals=c(0,0))
**> > >
**> > >You could try the recent package BB by Ravi Varadhan. The code could
**> > >be the following:
**> > >
**> > >library(BB)
**> > >
**> > >f <- function(x) {
**> > > x1 <- x[1]
**> > > x2 <- x[2]
**> > >
**> > > F <- rep(NA, 2)
**> > >
**> > > F[1] <- x1^2 - x2^2 - 6
**> > > F[2] <- x1 - x2 - 3
**> > >
**> > > return(F)
**> > >}
**> > >
**> > >p0 <- c(1,2)
**> > >dfsane(par=p0, fn=f,control=list(maxit=3000))
**> > >
**> > >I got the solution:
**> > >
**> > >x1 = 2.5
**> > >x2 = -0.5
**> > >
**> > >Paul
**> > >
**> >
**> >
**> > >______________________________________________
**> > >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.
**> > >
**> >
**> > ______________________________________________
**> > 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.
**> >
**>
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