[R-sig-finance] Distribution Fitting and fitdistr()

[Lorenzo Isella]

Dear All,
I think I understood how to use the fitdistr() function to fit random
draws to a certain distribution.
I first tested it on a unimodal Gaussian distribution:

rm(list=ls())
library(MASS)
set.seed(123)
mydata<-rnorm(10000,2.0,4.0)
gauden<-function(x,mu,sig)
{
1/(sqrt(2*pi)*sig)*exp(-1/(2*sig^2)*(x-mu)^2)
}
myfit<-fitdistr(mydata,gauden,start=list(mu=5.0,sig=5.0),upper=c(20,20))
myfit2<-fitdistr(mydata,"normal")

seeing the (expected) agreement between myfit and myfit2.

Then I tested it on a set of draws from a mixture made up of three
Gaussian distributions.
This time I used 9 fitting parameters:
- 3 weights N1,N2,N3 for the components of the Gaussian mixture
- 3 standard deviations sig1,sig2,sig3
- 3 means mu1,mu2,mu3

Here is the code I used:

rm(list=ls()) 
library(MASS)
set.seed(123)
NN<-10000
three<-3 #number of gaussian sequences I want to generate
mysample<-matrix(nrow=NN,ncol=three)
sdvec<-seq(1:three)
sdvec[1]<-4
sdvec[2]<-3
sdvec[3]<-3.5
meanvec<-seq(1:three)
meanvec[1]<-20
meanvec[2]<-50
meanvec[3]<-70

for (i in 1:three)
{
 mysample[ ,i] <-rnorm(NN,meanvec[i],sdvec[i])
}
dim(mysample)<-c(3*NN,1)
plot(density(mysample,kern="gaussian"),lwd=2,col=300)

mydistr<-function(x,mu1,sig1,N1,mu2,sig2,N2,mu3,sig3,N3)
{
N1/(sqrt(2*pi)*sig1)*exp(-1/(2*sig1^2)*(x-mu1)^2)+
N2/(sqrt(2*pi)*sig2)*exp(-1/(2*sig2^2)*(x-mu2)^2)+
N3/(sqrt(2*pi)*sig3)*exp(-1/(2*sig3^2)*(x-mu3)^2)
}
myfit<-fitdistr(mysample,mydistr,start=list(sig1=2,sig2=2,sig3=2,
N1=0.3,N2=0.3,N3=0.4,mu1=25,mu2=55,mu3=76))

But this time the fitdistr() is not able to carry out the optimization
and the warnings do not tell (me at least) that much.
Am I mistaking something?  Furthermore, how can I be sure that the
optimization will lead to weights such that N1+N2+N3=1?
I have not been able to try the mixdist package or any other tool, but
any suggestion about how to fit this threemodal distribution (which
should not be rocket science for someone more experienced than myself)
is welcome.
Best Regards

Lorenzo