|
|
 | | From: | Roger Bagula | | Subject: | Re: Approximate entropy applied to the Pi digits | | Date: | Fri, 03 Dec 2004 21:06:31 GMT |
|
|
 |
--------------060303060104070306030604
Content-Type: text/plain; charset=us-ascii; format=flowed
Content-Transfer-Encoding: 7bit
There's something wrong with this set of functions.
A friend has programmed a better function but I can't post it.
Roger Bagula wrote:
>
>
> In Ivars Peterson's MathTrek - Randomness, Risk, and Financial Markets:
>
> http://www.maa.org/mathland/mathtrek_10_11_04.html
> I found the reference to Steven M. Pincus' Approximate entropy.
> I applied it to Hofstader's sequence, the last digits of the primes
> and Pi's digits
> and the Approximate entropy came out larger in that order.
> My program is really slow, but it does seem to give the ApEn function as
> defined in the paper. It is a lot like a Lyapunov Largest exponent
> in the way I've calculated it, but it more a probability measure
> on the variables than a direct result of the variables. It is also
> much harder
> and takes longer than a Lyapunov since it has two distinct sums in it.
> It is more closely related to correlation dimension that Kaplan-York
> dimension
> in it's method of calculation.
>
> Clear [f,n,d,c,Phi,ApEn,a,i,j,k,r,m,g,digits]
> (*Steven M. Pincus,Approximate entropy as a measure of system complexity,
> PNAS,vol 88,pp2297-2301,March 1991,Mathematics*)
> digits=100
> $MaxExtraPrecision =digits
> f[n_]:=Floor[Mod[10^n*Pi,10]]
> (* approximate Entropy for Pi digits sequence*)
> d[i_,j_,m_,n_]:=Max[Table[Abs[f[i+k-1]-f[j+k-1]],{k,1,m-1}]]
> c[i_,r_,m_,n_]:=N[Sum[If[d[i,j,m,nTrue]
> y=Fit[a,{1,x},x]
> gb=Plot[y,{x,1,digits}]
> Show[{ga,gb}]
>
> Respectfully, Roger L. Bagula
>
> tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel:
> 619-5610814 :
> alternative email: rlbtftn@netscape.net
> URL : http://home.earthlink.net/~tftn
>
>
>
>
> ------------------------------------------------------------------------
>
--
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn@netscape.net
URL : http://home.earthlink.net/~tftn
--------------060303060104070306030604--
|
|
|
