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Topic: problem on record-breaking values in probability
Replies: 14   Last Post: Apr 14, 2013 11:36 PM

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 David Bernier Posts: 3,892 Registered: 12/13/04
Re: problem on record-breaking values in probability
Posted: Feb 27, 2013 5:49 AM

On 02/27/2013 05:31 AM, David Bernier wrote:
> I used Marsaglia's 64-bit SUPER KISS pseudo-random number generator
> to simulate uniform r.v.s on [0, 1] that are independent, as
> X_1, X_2, X_3, ad infinitum
>
> For each go, (or sequence) I define its 1st record-breaking value
> as R(1) as X_1, its 2nd record-breaking value R(2) as the
> value taken by X_n for the smallest n with X_n > X_1, and in general
> R(k+1) as the value taken by the smallest n with X_n > R(k), for

I'm a sinner .

That should be:
"R(k+1) as the value taken by X_n for the smallest n with X_n > R(k)"

> k = 2, 3, 4, 5, ...
>
> In my first simulation I get: R(20) = 0.999999999945556
> or about 5.4E-11 less than 1 , a one in 18 billion event.
>
> In fact, R(20) is about 1 - (0.307)^20 ...
>
> So, I'm wondering about the asymptotics of 1 - R(k) for very
> large k. Of course, R(k) is a andom variable with a
> probability distribution. Can we say something about the
> asymptotics of 1 - R(k) for large k?
>
> David Bernier
>

--
dracut:/# lvm vgcfgrestore
File descriptor 9 (/.console_lock) leaked on lvm invocation. Parent PID
993: sh
Please specify a *single* volume group to restore.

Date Subject Author
2/27/13 David Bernier
2/27/13 David Bernier
2/27/13 David Bernier
2/27/13 James Waldby
2/27/13 David Bernier
3/1/13 David Bernier
3/1/13 David Bernier
3/10/13 David Bernier
3/10/13 David Bernier
3/11/13 James Waldby
3/11/13 David Bernier
4/13/13 David Bernier
4/14/13 David Bernier
4/14/13 David Petry