Date: Apr 14, 2013 11:36 PM
Author: David Petry
Subject: Re: problem on record-breaking values in probability
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?