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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 Petry Posts: 1,104 Registered: 12/8/04
Re: problem on record-breaking values in probability
Posted: Apr 14, 2013 11:36 PM

On Wednesday, February 27, 2013 2:31:48 AM UTC-8, David Bernier wrote:

> uniform r.v.s on [0, 1] ... 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
> k = 2, 3, 4, 5, ...

> 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?

Wouldn't the probability distribution for 1-R(k) be very very closely related to the probability distribution for the product of 'k' uniformly distributed random variables?

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