Re: Data Range given mean and std deviation values

In article <ef2c194.-1@xxxxxxxxxxxxxxxx>, "weihua xiong"
<weihuax@xxxxxxxxx> wrote:

Hi:

If we are given the mean of a datset is '0', the std deviation value
is 'std_dev', this data set is assumed to be gaussian distribution.
Can we predict the range of the dataset, that is, the possible
minimal and maximal values in the data set.
--------------------
Weihua, can we assume that your data values are mutually independent
random variables? That isn't clear from your statement. And when you
refer to the "range" of your values, are you referring to the expected
values of their maximum and minimum values? If so, then the cumulative
probability for the maximum value, for example, can be expressed as:

P(max(x1,x2,...,xn)<=a) = (1/sqrt(2*pi)*int(exp(-t^2/2),'t',-inf,a)^n

where the data set has the n random variables x1, x2, ..., xn. This is
the n-th power of the single Gaussian variable cumulative probability.

The trouble is that I haven't yet managed to see a convenient way of
evaluating the expected value of this distribution. It is clearly greater
than zero for n greater than 1 and is almost surely something finite. The
larger n is, the larger the expected value will be. I see that it can be
converted into something in terms of incomplete gamma functions but it
will require more work to yield a form that can readily be computed.
Analogous statements can be made about the minimum value distribution.

I await your assurance that the answers to the above two questions are
"yes" before going any further.

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

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