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To: python-list@python.org
From: Dennis Lee Bieber <wlfraed@ix.netcom.com>
Subject: Re: Testing random
Date: Sun, 07 Jun 2015 11:04:37 -0400
Organization: IISS Elusive Unicorn
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On Sun, 07 Jun 2015 08:27:59 +0200, Cecil Westerhof <Cecil@decebal.nl>
declaimed the following:

>
>It shows that when the first parameter increases the deviation
>increases and when the second parameter increases the deviation
>decreases. Exactly what you would expect. But what are the ranges you
>would expect with a good random function. Then it could be used to
>test a random function.

	From what I could make out, you are testing the distribution of an
equally weighted function (that is, any value in the lower..upper range is
equally likely to appear).

	Unfortunately, a measure of distribution shows nothing for
predictability (non-randomness).

	Here's an example displaying ideal distribution (I should have made the
first for-loop a generator)

>>> def lin(smpl=10000):
... 	samples = {}
... 	for i in range(smpl):
... 		samples[i % 10] = samples.get(i % 10, 0) + 1
... 	for i in range(10):
... 		print i, samples[i]
... 		
>>> lin()
0 1000
1 1000
2 1000
3 1000
4 1000
5 1000
6 1000
7 1000
8 1000
9 1000
>>> lin(9876)
0 988
1 988
2 988
3 988
4 988
5 988
6 987
7 987
8 987
9 987
>>> 

	But is it random? Only in that there is a finite chance of a truly
random sequence being: 0, 1, 2, 3, 4, ..., 8, 9, 0, 1, ...

	If the distribution is widely uneven, the odds are the generator is not
random -- or at least, not random in the equally weighted sense; it may be
perfectly random gaussian or Poisson distribution.

	For the equally weighted case, one may need to also compute, say,
differences between adjacent samples, between alternate samples, between
every 10th sample, whatever... with the intent being to reveal if there is
any cyclic pattern detectable.
-- 
	Wulfraed                 Dennis Lee Bieber         AF6VN
    wlfraed@ix.netcom.com    HTTP://wlfraed.home.netcom.com/