Needed: Understading runif() output :-)

Thu, May 25, 2000 9:58 AM

I don't think this is a problem with the RNG.  There are only 2^32 numbers
(2^31 in some systems)that can be represented with a 32-bit floating point
number.  So, a rough back-of-the-envelope calculation gives me:

[1] 10.73742

i.e. about 10-11 possible numbers bigger than .9999999975 which seems to be
your threshold.  So the results you get aren't very surprising.

# David Smith

--
David M Smith <dsmith at splus.mathsoft.com>
S-PLUS Product Manager, MathSoft DAPD, Seattle WA
Tel: +1 (206) 283 8802 x360
Fax: +1 (206) 283 0347

-----Original Message-----
From: owner-r-help at stat.math.ethz.ch
[mailto:owner-r-help at stat.math.ethz.ch]On Behalf Of Kjetil Kjernsmo
Sent: Thursday, May 25, 2000 07:39
To: R Help list
Subject: [R] Needed: Understading runif() output :-)

Dear all,

I have been trying to understand what runif() is telling me.
I am generating lots of numbers (billions and billions (wow,
I've dreamed
about saying that for many years... :-) ), for a distribution
that has the
following quantile function:
    1 / (2 * sqrt(1 - p))
(that is, the distribution has a lower cutoff)
As you can imagine, this has rather heavy upper tail. I was
looking at the
largest values, and it looked as if the largest values
appeared again and
again. Now, it wasn't in itself that large values were
strange, since I'm
generating so many numbers, but that the largest were very much larger
than the second largest numbers, and that exactly the same
number appeared
again and again. First I thought it was a bug, and I'm sorry to have
wasted r-devels time with a bug report.

I started running the same simulation with different RNGs and they all
seem to generate numbers in "quantized states". Then, I
started to look
into what runif() gives, and let it print 13 digits.
In the below output, I use the "Mersenne-Twister" RNG and I
have generated
1e+10 numbers (100000 at a time) and I print a line if it the
number is
above 10000 (my dist, the left coloumn), the right coloumn are runif()
the corresponding outputs.
[1] 3.276800000000e+04 9.999999997672e-01
[1] 13377.479981919865     0.999999998603
[1] 1.158523750296e+04 9.999999981374e-01
[1] 1.036215143684e+04 9.999999976717e-01
[1] 1.158523750296e+04 9.999999981374e-01
[1] 1.036215143684e+04 9.999999976717e-01
[1] 1.036215143684e+04 9.999999976717e-01
[1] 13377.479981919865     0.999999998603

So, it seems that the runif() outputs are "quantized" too.
The question
is: What is the reason for this?
I have been playing with the tought that it may be connected
to the finite
number representation capabilites of a computer? As I said,
all the RNGs
seems to have similar characteristics.

If this is the case, I have no problem. It's cosmology I'm doing, so
whether a number is 32768 or 29923 is (presumably) of little
importance. However, I should understand what is going on here.... :-)

Finally, I may get a "loss of precision"-problem in my coding of my
quantile function, but I guess it is not that much of a concern.

Hope somebody can help me with this.

Best,

Kjetil
--
Kjetil Kjernsmo
Graduate astronomy-student                    Problems worthy
of attack
University of Oslo, Norway            Prove their worth by
hitting back
E-mail: kjetikj at astro.uio.no                                -
Piet Hein
Homepage <URL:http://www.astro.uio.no/~kjetikj/>
Webmaster at skepsis.no

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Needed: Understading runif() output :-)

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