Date:         Mon, 15 Sep 1997 15:10:07 -0700
Reply-To:     Scott Carl <SCARL@THECREEK.COM>
Sender:       "SAS(r) Discussion" <SAS-L@UGA.CC.UGA.EDU>
From:         Scott Carl <SCARL@THECREEK.COM>
Subject:      Re: random numbers + random walk | bug?
Comments: To: Bernard Tremblay <bernard@CAPITALE.QC.CA>
Content-Type: text/plain

You are correct Bernard. The symmetric random walk is a recurrent Markov
Chain when the dimension is less than three. Here is my version of the
simulation:
 
data testit;
        do bootstrp=1 to 10;
          position=0;*Start at 0;
          do loop=1 to 10000;
                move=2*(ranbin(425435532,1,.5))-1;
                position+move;
                output;
          end;
        end;
proc means;
        by bootstrp notsorted;
        var position;
        output out=out;
proc means;
        var position;
        where _stat_="MEAN";
run;
quit;
 
 
 
Scott Carl
Marketing Statistician
Coldwater Creek
One Coldwater Creek Drive
Sandpoint, ID 83864
scarl@thecreek.com
(208) 265-7136
 
 
 
> ----------
> From:         Bernard Tremblay[SMTP:bernard@CAPITALE.QC.CA]
> Sent:         Monday, September 15, 1997 4:59 AM
> To:   SAS-L@UGA.CC.UGA.EDU
> Subject:      Re: random numbers + random walk | bug?
>
> Hi,
>         Are you sure of your resulting mean "sqrt(n)".  Since the
> probability
> of going left is the same as the probability of going right, on the
> average
> you should be at the same point ie ZERO...  May be the hypothesis is
> talking
> about the standard deviation ???? not the mean ????  Or may be your
> random
> walk should be on a plane ( 2 dimensions) instead of a line ?
>
>         Any random walker with some light here ???
>
>                 Regards,
>                         Bernard Tremblay
>           \\\|///
>         \\  - -  //
>          (  @ @  )
> +------oOOo-(_)-oOOo----------+---------------------------------+
> |  Bernard Tremblay           |                                 |
> |             La Capitale     | Tel:  (418) 646-2401            |
> |                             | Fax:  (418) 646-5960            |
> |                             | Int:  bernard@capitale.qc.ca    |
> +-----------------------------+---------------------------------+
> |             Imaginasys enr  | Res:  (418) 878-4447            |
> |                             | Int:  bertrem@quebectel.com     |
> +---------------Oooo----------+---------------------------------+
>         oooO   (   )
>        (   )    ) /
>         \ (    (_/
>          \_)
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> ~~~~~~~~
> >>>From owner-sas-l@UGA.CC.UGA.EDU Mon Sep 15 15:37 EDT 1997
> >>>Nntp-Posting-Host: cooch.biol.sfu.ca
> >>>X-Newsreader: Forte Free Agent 1.11/32.235
> >>>Xref: paladin.american.edu comp.soft-sys.sas:42841
> >>>Date:         Mon, 15 Sep 1997 15:48:14 GMT
> >>>From: Evan Cooch <cooch@FRASER.SFU.CA>
> >>>Subject:      Re: random numbers + random walk | bug?
> >>>To: SAS-L@UGA.CC.UGA.EDU
> >>>
> >>>>
> >>>>data test;
> >>>>  do loop=1 to 1000;
> >>>>    position=0;
> >>>>    do step=1 to 625;
> >>>>      choice=uniform(-1);
> >>>>      if choice<=0.5
> >>>>        then position=position-1;
> >>>>        else position=position+1;
> >>>>    end;
> >>>>    output;
> >>>>  end;
> >>>>run;
> >>>>
> >>>
> >>>
> >>>I tried this code, and several other permutations. Nothing works.
> The
> >>>math is clear. On average, for a 1-D random walk, you should be
> >>>sqrt(N) units away from where you started.
> >>>
> >>>Unfortunately, I don't even get close. I find this totally bizarre.
> >>>
> >>>Still puzzled...
> >>>
>