Re: newbie is looking for a customDistribution function

• To: mathgroup at smc.vnet.net
• Subject: [mg50413] Re: newbie is looking for a customDistribution function
• From: "Michael Taktikos" <michael.taktikos at hanse.net>
• Date: Thu, 2 Sep 2004 04:34:51 -0400 (EDT)
• References: <ch3o86\$t96\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In[1]:=  lst={a,a,b,c,a,d,a,c,c,a};

In[2]:=
twocombsLstDistribution[l_]:=
Module[{tc,oc, distro,d},
tc=Distribute[Table[Union[l],{2}],List];
oc[x_List] := Count[Partition[l, 2, 1], x];
distro=Map[oc,tc];
d=Apply[Plus, distro];
Table[{tc[[i]],N[distro[[i]]/d]},{i,1,Length[tc]}]]

In[3]:= twocombsLstDistribution[lst]

Out[3]=
{{{a,a},0.111111},{{a,b},0.111111},{{a,c},0.111111},{{a,d},0.111111},{{b,a},
0.},{{b,b},0.},{{b,c},0.111111},{{b,d},0.},{{c,a},0.222222},{{c,b},
0.},{{c,c},0.111111},{{c,d},0.},{{d,a},0.111111},{{d,b},0.},{{d,c},
0.},{{d,d},0.}}

(* {a,a} occurs with 0.111111 or 11.11%, {c,a} with 22.22%, {d,b} with 0% *)

Greetings from Hamburg,

Michael Taktikos

"János" <janos.lobb at yale.edu> schrieb im Newsbeitrag
news:ch3o86\$t96\$1 at smc.vnet.net...
> Hi,
>
> I looked for it in the archives, but found none.  I am looking for ways
> to create a custom distribution, which I can call as a function.  Here
> is an example for illustration.  Let's say I have a list created from a
> 4 elements alphabet  {a,b,c,d}:
>
> In[1]:=
> lst={a,a,b,c,a,d,a,c,c,a}
>
> Out[1]=
> {a,a,b,c,a,d,a,c,c,a}
>
> Distribute gives me - thanks David Park - all the two element
> combinations of {a,b,c,d}
>
> In[11]:=
> twocombs=Distribute[Table[{a,b,c,d},{2}],List]
>
> Out[11]=
> {{a,a},{a,b},{a,c},{a,d},{b,a},{b,b},{b,c},{b,d},{c,a},{c,b},{c,c},{c,d}
> ,{
>    d,a},{d,b},{d,c},{d,d}}
>
> I can count the occurrence of an element of twocombs in lst with the
> following function:
>
> occuranceCount[x_List] := Count[Partition[lst, 2, 1], x]
>
> Mapping this function over twocombs gives me the number of occurances
> of elements of twocombs in lst:
>
> In[12]:=
> distro=Map[occuranceCount,twocombs]
>
> Out[12]=
> {1,1,1,1,0,0,1,0,2,0,1,0,1,0,0,0}
>
> It shows that for example {c,a} occurs twice, {d,a} occurs once and
> {d,c} or {d,d} never occur.
>
> Now, I would like to create a distribution function called
> twocombsLstDistribution which I could call and it would give me back
> elements of twocombs with the probability as they occur in distro, that
> is for on average I would get twice as much {c,a}s as {d,a}s and never
> get {d.c} or {d,d}.
>
> How can I craft that ?
>
> /Of course I need it for an arbitrary but finite length string lst over
> a fixed length alphabet {a,b,c,d,....} for k-length elements of kcombs,
> and it has to be super fast  :).  My real lst is between 30,000 and
> 70,000 element long over a four element alphabet and I am looking for k
> between 5 and a few hundred. /
>
> János
> -------------------------------------------------
> People never lie so much as after a
> hunt, during a war or before an election
> - Otto von Bismarck -
>

```

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