Re: Testing a Pseudo-Random Generator


Luis A. Afonso wrote:

Luis, lease allow me to interject a few comments on what appears to be
an unnecessary
squabble because of your ambiguous use of the English language in
statistical terms.
You wrote:

LA> Its aim is merely to "illustrate" that how the difference of
normal sample means behave.

Perfect, so far.

LA> Theory demonstrate that the difference of means of two random
samples drawn
LA> from a standard normal Population (i.e. mean=0, sd=1) has a
Student distribution
LA> which df is the sizes sum minus 2.

This is the part that's caused Allen's comment, which is also not
completely
on target, even though his statement about linear combinations of
normals
is correct:

> Allen wrote:
>
>
> >Wrong. Linear combination of normals => normal. T >distribution
comes
> >from dividing by the square root of a chi-square (which >your code
does).

Now let's go back to your statement and CORRECT the
ambiguously/incorrectly
stated parts:

LA> Theory demonstrate that the difference of means of two random
samples drawn
LA> from a standard normal Population (i.e. mean=0, sd=1) has a
Student distribution
LA> which df is the sizes sum minus 2.

THEORY: The difference of means of two random samples drawn from
N(0,1), say
sample sizes n1 and n2, are the following:

The random variable X1bar ~ N(0, 1/sqrt(n1)).
The SAMPLING distribution of X1bar is T with (n-1) d.f.

The DIFFERENCE of the random variables X1bar and X2bar is also normal.
The SAMPLING distribution of (X1bar - X2bar) has a T with (n-2) d.f.

>
> My comment:
>
> What a confusion! Linear combination of normals? Absolutely not.

You are wrong here. The RANDOM VARIABLE which is a linear combination
of
normals is always normal.

> I simulated pairs of (independent) normal samples each of size 10
(yes, not 20,
> inattention) and found (by repetition) the experimental confidence
interval.

There, you are talking about what you observed in the SAMPLING
distribution of
two independent samples of size 10 each.


> I am less interested (as an practical statistician) to learn about to
find a
> good RNG than to test my <spade> ... since I have not a <tractor>.

Yes, but as a technician, you should know the difference between a
"spade" and
a "shovel", and a "tractor" from a "lawn mover". :)


> I know "The Art of Computing" since the 80`s , thanks by the
advise, even so.

When you were 80 years old? <G> <-- that meant it's a joke.

I have read several of your posts, I think much of your posts suffer
from similar
kind of ambiguity/misunderstanding because of your use of the ENGLISH
language,
especially relative to statistical terms.

-- Bob.

.