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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: 3,210
Registered: 12/13/04
Re: problem on record-breaking values in probability
Posted: Feb 27, 2013 7:10 AM
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On 02/27/2013 05:49 AM, David Bernier wrote:
> 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.


5.4E-11 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 record-breaking value, on my
second sequence, but it took much longer. The values
1 - R(20), one per sequence, are what I call "p-values"

from the simulations so far, a lot of variance in orders
of magnitude:

the corresponding p-value is 0.000000000054 // seq. 1
the corresponding p-value is 0.000000000001 // seq. 2
the corresponding p-value is 0.000000002463
the corresponding p-value is 0.000000000782
the corresponding p-value is 0.000000106993
the corresponding p-value is 0.000000342142
the corresponding p-value is 0.000000001978
the corresponding p-value is 0.000000017718
the corresponding p-value is 0.000000006582
the corresponding p-value is 0.000000002610
the corresponding p-value is 0.000000000231
the corresponding p-value is 0.000000001903
the corresponding p-value is 0.000000000084
the corresponding p-value is 0.000000000231
the corresponding p-value is 0.000000000018
the corresponding p-value is 0.000000033070
the corresponding p-value is 0.000000655701
the corresponding p-value is 0.000004194496
the corresponding p-value is 0.000002536667
the corresponding p-value is 0.000000003679
the corresponding p-value is 0.000000460191
the corresponding p-value is 0.000000000030
the corresponding p-value is 0.000000005678
the corresponding p-value is 0.000000530638
the corresponding p-value is 0.000000000208
the corresponding p-value is 0.000001879293
the corresponding p-value is 0.000000003686
the corresponding p-value is 0.000000107942
the corresponding p-value is 0.000000000096
the corresponding p-value is 0.000001509795
the corresponding p-value is 0.000000932180
the corresponding p-value 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.



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