Mixture of Distributions

I just realised I made a bad mistaqke (see below)

On 21-Feb-08 20:58:25, Evgenia wrote:

Dear R users, 
I would like to sample from a mixture distribution
p1*f1+p2*f2+p3*f3 with f1,f2,f3 three different forms
of distributions. I know that in the case of two
distributions I have to sample the mixture compoment
membership.

How can I weight my three distributions with their
respective probabilities?

Evgenia

There are several ways in which you could write code
to do this, but all amount to the fact that each value
sampled from such a mixture is obtained by
a) choose between f1, f2, f3 at random according to the
   probabilities p1, p2, p3 (it is assumed p1+p2+p3=1).
b) sample 1 value from whichever of f1, f2, f3 was chosen.

Suggestion:

Suppose the functions rf1(n), rf2(n), rf3(n) respectively
sample n values from f1, f2 and f3.

S0 <- cbind(rf1(n),rf2(n),rf3(n))
ix <- sample(c(1,2,3),n,3,prob=c(p1,p2,p3),replace=TRUE)

So far so good!

S  <- S0[,ix]

But this will not do what I intended (i.e. select element ix[1]
from the first row os S0, ix[2] from the second row, and so on).

Instead, it will return an nxn matrix with n rows, and n columns
which are copies of columns of S0 in the order selected by ix!

The following will do the correct thing, though there must
be a neater way of doing it! The example below has been
corrected.

S <- S0[,1]*(ix==1) + S0[,2]*(ix==2) + S0[,3]*(ix==3)

will produce n values, each of which is a sample of size 1
from the mixture.

Example:

rf1 <- function(n){rnorm(n,0,1)} ## normal distribution with mean=0
rf2 <- function(n){rnorm(n,4,1)} ## normal distribution with mean=4
rf3 <- function(n){rnorm(n,9,1)} ## normal distribution with mean=9

p1 <- 0.2; p2 <- 0.3; p3 <-0.5
S0 <- cbind(rf1(500),rf2(500),rf3(500))
ix <- sample(c(1,2,3),500,prob=c(p1,p2,p3),replace=TRUE)
S <- S0[,1]*(ix==1) + S0[,2]*(ix==2) + S0[,3]*(ix==3)

hist(S,breaks=50)

Hoping this helps.
Ted.

And again!
Ted.

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E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
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Date: 21-Feb-08                                       Time: 22:20:04
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