[R] Probabilistic aggregation

[Petr Savicky]

On Mon, May 14, 2012 at 11:15:18PM -0700, davewiz wrote:
> Hello, I'm a new user to R and need some help coding a mathmatically simple
> aggregation of normal distributions. I have three normal distributions:
> A ~ N(8.51, 4.24^2)
> B ~ N(7.57, 3.62^2)
> C ~ N(10.84, 6.59^2)
> with correlation coefficients of:
> rho(AB) = 0.710
> rho(AC) = 0.263
> rho(BC) = 0.503
> and I want to simulate Z = A + B + C, showing the results on a plot and
> fitting a distribution to the simulated data.

Hi.

First, derive the covariance matrix for the joint distribution.
Then, use the formulas from section Affine transformation of

  http://en.wikipedia.org/wiki/Multivariate_normal

to derive the mean and variance of the variable A + B + C.
Taking a sum of coordinates is an affine transformation
represented by the matrix with one row of all ones, i.e.

  B = (1, 1, 1)

For generating Z, use the function rnorm(), for computing the
sample mean and sample estimate of the standard deviation, use
functions mean() and sd().

Hope this helps.

Petr Savicky.