Re: newbie is looking for a customDistribution function

• To: mathgroup at smc.vnet.net
• Subject: [mg50395] Re: newbie is looking for a customDistribution function
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 2 Sep 2004 04:34:19 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <ch3o86\$t96\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

you as for the inverse method to generate random numbers.
In you case you want to have random numbers due to the distribution

f[n_]:=Plus @@ Take[distro,n]/(Plus @@ distro)

because the table you call "distro" is the density and not the
distribution function.

f[n] is a real number between [0,1) and if you wish to create
random numbers with this distribution function you can generate
a uniform random number q and look for the interval
f[m-1]<= q <f[m]. The integer value m with is you random variable
with distribution function f.

Regards
Jens

János wrote:
>
> 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. /
>