Re: Covariance matrix from standard deviations

In article <ef2d5a6.-1@xxxxxxxxxxxxxxxx>, "Cheetan Sharma"
<csharma@xxxxxxxxxx> wrote:

Hi,

I have an array with standard deviations of a group of variables. Is
there any way that I can calculate the variance-covariance matrix
from this? Any help would be appreciated.

Thank you,

CS
--------------------
Variances, yes, but covariances between different random variables, no!
Covariance values depend on whatever dependencies exist between the random
variables, and the fact that the individual variables are of normal
distribution with some given mean and standard deviation tells us nothing
about their mutual dependence. In fact, unless it is given, there is no
reason to suppose that the variables are even jointly normal; that is
already a particular restriction on their mutual dependence. At one
extreme they could be mutually independent, in which case each of their
covariances would be zero. At the other extreme, all the random variable
pairs could have a correlation of one, so that the covariance for each
pair would equal the square root of the product of their two variances -
that is, with probability one, knowing any one of their values would
determine all the others' values. These two extremes illustrate the wide
range of possibilities that exist for a set of normally distributed random
variables with given means and variances.

To summarize: in any set of jointly normal random variables the set of
means, variances, and covariances are all essential in determining the
random variables' joint distribution.

(Remove "xyzzy" and ".invalid" to send me email.)
Roger Stafford
.

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