R help - Nov 2013 - Regression of the sum of distributions on an histogram with R

Dear all,

I hope that is the right list for my question

Here is the case:

I want to describe an histogram as the sum of several distributions, and
thus to fit these distributions on that histogram. In ROOT/C++ that is
pretty obvious, but I look for the equivalent in R. Here is a
self-explanatory exemple:

## SUM OF TWO GAUSSIANS OF DIFFERENT WIDTHS
x=rnorm(n=1000,mean=0,sd=1)
y=rnorm(n=1000,mean=0,sd=3)
z=append(x,y)
b=seq(-10,10,by=0.25)
hist(z,breaks=b)

In this case the individual contributions (x) and (y) are known, and I can
extract their density curves with a Kernel:

## NARROW GAUSSIAN
hist(x,prob=T,breaks=b)
dx=density(x,ker="epan")
lines(dx,col=3,lwd=2)
## WIDE GAUSSIAN
hist(y,prob=T,breaks=b)
dy=density(y,ker="epan")
lines(dy,col=2,lwd=2)

I would like to do something like z~dx+dy

Where the fractions of dx and dy would be the parameters to be fitted.
Looking into the R documentation I have only found references to single
regression and smoothing.

Does anyone have a clue or a sympathetic link?

I found various tools, but either they assume Gaussian distributions, or,
as mixtools, they don't accept user-defined functions.


Thanks in advance,


X.



-- 


*---------------------------------------Xavier Prudent*


*Computational biology and evolutionary genomics*

*Guest scientist at the Max-Planck-Institut für Physik komplexer Systeme*
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