
Re: problem on recordbreaking values in probability
Posted:
Feb 27, 2013 7:10 AM


On 02/27/2013 05:49 AM, David Bernier wrote: > 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.
5.4E11 is reported below with this comment: // seq. 1 for "sequence 1" .
>> >> In fact, R(20) is about 1  (0.307)^20 ...
I finally got another 20th recordbreaking value, on my second sequence, but it took much longer. The values 1  R(20), one per sequence, are what I call "pvalues"
from the simulations so far, a lot of variance in orders of magnitude:
the corresponding pvalue is 0.000000000054 // seq. 1 the corresponding pvalue is 0.000000000001 // seq. 2 the corresponding pvalue is 0.000000002463 the corresponding pvalue is 0.000000000782 the corresponding pvalue is 0.000000106993 the corresponding pvalue is 0.000000342142 the corresponding pvalue is 0.000000001978 the corresponding pvalue is 0.000000017718 the corresponding pvalue is 0.000000006582 the corresponding pvalue is 0.000000002610 the corresponding pvalue is 0.000000000231 the corresponding pvalue is 0.000000001903 the corresponding pvalue is 0.000000000084 the corresponding pvalue is 0.000000000231 the corresponding pvalue is 0.000000000018 the corresponding pvalue is 0.000000033070 the corresponding pvalue is 0.000000655701 the corresponding pvalue is 0.000004194496 the corresponding pvalue is 0.000002536667 the corresponding pvalue is 0.000000003679 the corresponding pvalue is 0.000000460191 the corresponding pvalue is 0.000000000030 the corresponding pvalue is 0.000000005678 the corresponding pvalue is 0.000000530638 the corresponding pvalue is 0.000000000208 the corresponding pvalue is 0.000001879293 the corresponding pvalue is 0.000000003686 the corresponding pvalue is 0.000000107942 the corresponding pvalue is 0.000000000096 the corresponding pvalue is 0.000001509795 the corresponding pvalue is 0.000000932180 the corresponding pvalue is 0.000000000058
 dracut:/# lvm vgcfgrestore File descriptor 9 (/.console_lock) leaked on lvm invocation. Parent PID 993: sh Please specify a *single* volume group to restore.

