[R] Non-linear system of equations
Radka Pancheva
radica at abv.bg
Fri Apr 25 14:12:45 CEST 2008
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
>
>______________________________________________
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>
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