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Re: bimodal distribution in sign of difference of Pi digits]
*To*: mathgroup at smc.vnet.net
*Subject*: [mg51725] Re: bimodal distribution in sign of difference of Pi digits]
*From*: Roger Bagula <tftn at earthlink.net>
*Date*: Sun, 31 Oct 2004 01:15:46 -0500 (EST)
*Reply-to*: tftn at earthlink.net
*Sender*: owner-wri-mathgroup at wolfram.com
Dear jasonp,
I don't know.
This method is a new way to investigate Pi digits.
I had done some counts of base ten digits frequencies before this.
I have no real explaination of why the difference is higher in higher number of digits.
The groups of positive "Sign"s should
random. It is Sign[x]-> {-1,0,1} depending on the difference in consecutive
differences. It is the probability of a digit pair:
{a,b}--> Sign[a-b]
p=Probability [a]*Probability[b]
If they are equal as p0:
p->p0^2
If the Mathematica for such a probability would be:
p0->Random[Integer,{0,9}] as a Distribution
Since this is an straight type probabilty and not a Gaussian
the probabilies are equal and should be over a long term
1/10 each or a total of
p-->1/100
different for different combinations:
{a>b}->+1,{a-1},{a=b}->0
at {4/10,4/10,2/10} that gives something like
4/1000,4/1000,2/1000
I'm not seeing that kind of behavior except for the bimodal
which is expected as
(a=b) is
only about 2/10 of the 1/100 and I'm seeing more zeros than that.
It appears to be a much more complex distribution.
I want to try E and orther irrational numbers by this method as well!
I'm glad you asked as I hadn't thought to do a probability analysis
until now!
I can simulate the probability above in Mathematica
and see what I get
and compare them.
jasonp at boo.net wrote:
>Quoting Roger Bagula :
>
> >
>>(* Sum of the sign of the differences between the first 2000 digits of Pi*)
>> >>
>
>Shouldn't this behave like a random walk, i.e. the variance
>increases over time?
>
>jasonp
>
>
>------------------------------------------------------
>This message was sent using BOO.net's Webmail.
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>
> >
--
Respectfully, Roger L. Bagula
tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn at netscape.net
URL : http://home.earthlink.net/~tftn
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