
Re: problem on recordbreaking values in probability
Posted:
Feb 27, 2013 5:49 AM


On 02/27/2013 05:31 AM, David Bernier wrote: > I used Marsaglia's 64bit SUPER KISS pseudorandom 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 recordbreaking value > as R(1) as X_1, its 2nd recordbreaking 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 5.4E11 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.

