Re: Re: newbie is looking for a customDistribution function

*To*: mathgroup at smc.vnet.net*Subject*: [mg50429] Re: [mg50411] Re: [mg50383] newbie is looking for a customDistribution function*From*: DrBob <drbob at bigfoot.com>*Date*: Fri, 3 Sep 2004 03:35:27 -0400 (EDT)*References*: <200409010549.BAA29848@smc.vnet.net> <200409020834.EAA02102@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

More generally, any mapping of a finite measure space into the extended real line implies a measure on the Borel sets, giving rise to a distribution function. It isn't difficult to map the values of a List into the reals--to Range[Length[theList]], for instance. Given such an embedding, any probability measure on the original set implies a distribution function, and vice-versa. Anyway, the OP apparently wanted a sampling function, like Random[], which doesn't require computing a distribution function at all. He already knew (and described in his post) how to calculate relative frequencies. Bobby On Thu, 2 Sep 2004 04:34:45 -0400 (EDT), Tomas Garza <tgarza01 at prodigy.net.mx> wrote: >> From a formal point of view, a distribution function is defined on the > reals. You can't, therefore, define it on lists of two, three, or more > symbols. A frequency function, on the other hand, may be defined on any set > of events. But, then, it is rather trivial for your problem: once you have > your list distpro, just divide each value in the list by the sum of all the > values, and that's it. Or, maybe, I misunderstood your question? > > Tomas Garza > Mexico City > ----- Original Message ----- > From: "János" <janos.lobb at yale.edu> To: mathgroup at smc.vnet.net > To: mathgroup at smc.vnet.net > Subject: [mg50429] [mg50411] [mg50383] newbie is looking for a customDistribution function > > >> 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. / >> >> Thanks ahead, >> János >> ------------------------------------------------- >> People never lie so much as after a >> hunt, during a war or before an election >> - Otto von Bismarck - >> >> > > > > -- DrBob at bigfoot.com www.eclecticdreams.net

**References**:**newbie is looking for a customDistribution function***From:*János <janos.lobb@yale.edu>

**Re: newbie is looking for a customDistribution function***From:*Tomas Garza <tgarza01@prodigy.net.mx>

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**Re: newbie is looking for a customDistribution function**

**Re: newbie is looking for a customDistribution function**