Re: Why to call it pseudorandom?

From: Herman Rubin (hrubin_at_odds.stat.purdue.edu)
Date: 09/02/04 

Date: 2 Sep 2004 14:37:01 -0500

In article <41308afb$0$25605$afc38c87@news.optusnet.com.au>,
Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote:

>"David C. Ullrich" <ullrich@math.okstate.edu> wrote in message
>news:hl11j09t9o6cd9tvc9a6o32se65hhlofkq@4ax.com...
>> On 28 Aug 2004 05:55:20 -0700, luiroto@yahoo.com (Luis A. Rodriguez)
>> wrote:

>> >If an algorithm produces a infinte sequence of digits that never
>> >falls into a loop and passes the most stringent statistical tests
>> >about its uniformity, why to call it pseudorandom?

>> maybe because the digits are not random? if they're produced by
>> an algorithm then they're not unpredictable.

>> >If genius discover a system of equations for the roulette, the
>> >old "random" experiments made with roulettes will appear at daybreak
>> >as pseudorandom?

>> ************************

>> David C. Ullrich

>> sorry about the inelegant formatting - typing
>> one-handed for a few weeks...

>And at a practical level, all computer rand() generators loop. They take a
>seed n and calculate f(n), then f(f(n)) etc.

There are many more complicated ones, which also loop. The
"n" may be much more than one computer word.

>So they loop over whatever range n can take (at most). If n is a 32 bit
>integer - and it often is - it will loop over 4 billion numbers, probably
>enough to generate enough mineseweeper boards and bridge hands to keep most
>people happy.

Not enough for many applications. However, there are
generators with periods longer than all computations which
ever will be done, but they are not always adequate.

>Many rand() functions are however random according to all other statistical
>criteria.

Not "all other"; they fail the test of having zero
predictive power when tested against the algorithm.

There are an infinite number of statistical criteria,
and any finite sequence of outputs will fail some
of those criteria. The ones you think of are not
enough. 

-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558

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