[R] Probabilistic aggregation

[David L Carlson]

To generate multivariate normal distributions, you will want mvrnorm in
package MASS.

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Petr Savicky
> Sent: Tuesday, May 15, 2012 7:14 AM
> To: r-help at r-project.org
> Subject: Re: [R] Probabilistic aggregation
> 
> 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.
> 
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