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MathGroup Archive 2005

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Re: easy question about random numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53391] Re: easy question about random numbers
  • From: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>
  • Date: Sun, 9 Jan 2005 23:03:44 -0500 (EST)
  • References: <crqb7f$cak$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

You could use MultinomialDistribution. Here is an example:

<<Statistics`MultiDiscreteDistributions`

k = 10;
p = (#1/Total[#1] & )[Table[Random[], {k}]];
n = 1;
dist = MultinomialDistribution[n, p];

k is the number of states, p is the vector of state probabilities (in this 
case these are random numbers that sum to unity), and n is the number of 
trials.

You can then use Random[dist] to generate a histogram with k bins, and with 
the n trials placed in the appropriate bins. In this case (i.e. n=1) there 
is a 1 in one of the bins, and the rest of the bins contain 0.

If you use RandomArray[dist, m] you can generate the result of m evaluations 
of Random[dist].

Alternatively, if you don't mind lumping all of the results together in a 
single histogram (this wipes out knowledge of the order in which the trials 
occurred) you could set n = m in the first place, and then evaluate 
Random[dist] once. Here is how this works for n = 100:

k = 10;
p = (#1/Total[#1] & )[Table[Random[], {k}]];
n = 100;
dist = MultinomialDistribution[n, p];
Random[dist]

Steve Luttrell

"Pedrito" <pedrito6 at softhome.net> wrote in message 
news:crqb7f$cak$1 at smc.vnet.net...
> Hi everybody!
>
> I wanted to obtain a discrete random number generator that I needed for
> a project.
>
> On the library Statistics`DiscreteDistributions` I could find the 
> DiscreteUniformDistribution
> function. But I wanted to specify the probability for each one of the
> states.
>
>
> For instance:
> If we need to simulate an unfair dice, we could have this probabilities
> for each one of the sides:
> {1/6, 1/6, 1/6, 1/6, 9/60, 11/60}
>
> So I wrote:
> li2 = {1/6, 1/6, 1/6, 1/6, 9/60, 11/60}
> li3=FoldList[Plus,0,li2]
> Module[{i = 1, r = Random[]}, While[ !li3[[i]] < r < li3[[i + 1]], i++]; 
> i]
>
> It works ok but I don't know if there is another (better) way of doing
> this.
> Any suggestion?
> 



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