[R] Help on probability distribution question

[(Ted Harding)]

On 11-Oct-2012 17:22:44 Andras Farkas wrote:
> Dear All,
> I have a questions I would like to ask about and wonder if you
> have any thoughts to make it work in R.
> 
> 1. I work in the field of medicine where physiologic variables
> are often simulated, and they can not have negative values.
> Most often the assumption is made to simulate this parameters
> with a normal distribution but in the "log-domain" to avoid from
> negative values to be generated. Since the expected mean and SD
> is usually known from the normal domain, using the methods described
> in the wikipedia article "Arithmetric moments" I generate μand σ
> and simulate with rlnorm(). At times though the following issue
> comes up: I have the mean and SD for the parameters available
> from the normal domain, and the covariance matrix from the normal
> domain. Then I would like to simulate the values, but to avoid
> from negative values being generated I have to fall back on rlnorm
> in {compositions}. My issue is though that my covariance matrix is
> representing the covariance of the parameters in the normal domain,
> as opposed to in the lognormal domain. Any thoughts on how  to work
> around this?
> 
> apreciate the help,
> Andras

If I understand your question correctly, if Y is the variable being
simulated then you know the mean (M, say) and the variance (V, say)
of log(Y). So you can simulate X from a normal distribution with
mean M and variance V = S^2 (S = SD of X), and then Y = exp(X):

  Y <- exp(rnorm(n,M,S))

where n is the number of sampled values you want.

When Y is multivariate, with M the vector of means and V the
covariance matrix of log(Y), then use a similar approach with
the function mvrnorm() from the MASS package:

  library(MASS)
  Y <- mvrnorm(n,M,V)

Does this help?
Ted.

-------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding at wlandres.net>
Date: 11-Oct-2012  Time: 18:51:47
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