[R] Probabilistic aggregation

Petr Savicky savicky at cs.cas.cz
Tue May 15 14:13:39 CEST 2012


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.



More information about the R-help mailing list