Re: non-Markov base ten random number generator based on Pi

*To*: mathgroup at smc.vnet.net*Subject*: [mg52048] Re: non-Markov base ten random number generator based on Pi*From*: Bill Rowe <readnewsciv at earthlink.net>*Date*: Mon, 8 Nov 2004 03:13:41 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

On 11/7/04 at 1:03 AM, tftn at earthlink.net (Roger Bagula) wrote: >This result is an experimental random number generator. It uses the >PSLQ Bailey Pi digits rational polynomial to generate digits in the 0 >to 9 range using a process that loses information , but generally >behaves like the Pi digits. It is not Markov, in that there is no >previous behavior involved in calculating the next random number. >(* Bailey formula with digit drop base 80*) >(* base 10 random number generator that isn't Markov *) >(* use integer seed as the number of digits in to start calculation*) >(* other PSLQ functions of transcendental numbers could be used to do >this same kind of random number*) >f[n_]=Floor[Mod[80^n*(4/(8*n+1)-2/(8*n+4)-1/(8*n+5)-1/(8*n+6))/16^n,10]] >Digits=4000;rdpi=Table[f[n],{n,0,Digits}]; >c1=Drop[FoldList[Plus,0,Sign[Drop[rdpi,1]-Drop[rdpi,-1]]],1]; >ListPlot[c1,PlotJoined->True]; >(* Rowe Count*) >d1=Flatten@{0,Length/@Split[Sort@c1], 0} >Dimensions[d1][[1]] >ListPlot[d1,PlotJoined->True]; I gather from your various posts you are trying to use the plot of c1 as a visual indicator of randomness. If that is your goal, then there are far simpler plots that are more meaningful. One of the simplest and easiest to interpret would be a plot of the cumulative distribution function for the data set. For example: dataSize = 10000; data = Table[Random[Integer,{0,9}],{dataSize}]; ListPlot[ Rest@FoldList[Plus,0,Length/@Split[Sort@data]]/dataSize, PlotJoined->True]; For a uniform distribution, the cumulative distribution function is x/(b-a) where a, b are the end points. That is, the cumulative distribution function for a uniform distribution should plot as a straight line from 0 to 1 over the interval (a,b). Contrast this with <<Statistics`DiscreteDistributions`; data = Table[Random[BinomialDistribution[5, .5]], {dataSize}]; ListPlot[ Rest@FoldList[Plus,0,Length/@Split[Sort@data]]/dataSize, PlotJoined->True]; The plot is clearly not a straight line indicating the data is not from a uniform distribution. But to really demonstrate a pseudo random number generator adequately generates uniform deviates you will need more than such a simple plot. -- To reply via email subtract one hundred and four