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Re: Defining a distribution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg114794] Re: Defining a distribution
  • From: Barrie Stokes <Barrie.Stokes at newcastle.edu.au>
  • Date: Fri, 17 Dec 2010 03:29:33 -0500 (EST)
  • References: <201012161048.FAA11797@smc.vnet.net>

Hi Omri

Have a look at 

http://reference.wolfram.com/mathematica/ref/ProbabilityDistribution.html 

where you will find a distribution-defining statement via a given pdf such as:

dist = ProbabilityDistribution[(Sqrt[2]/Pi) (1/(1 + x^4)), {x, -Infinity, Infinity}];

You can then generally draw samples from "dist" via such as:

data = RandomVariate[dist, 10^5];

(see http://reference.wolfram.com/mathematica/ref/RandomVariate.html).

However, if you look at: http://reference.wolfram.com/mathematica/ref/ProbabilityDistribution.html, and try:

\[ScriptCapitalD] = 
  ProbabilityDistribution[2^(-x - 1), {x, 0, \[Infinity], 1}]; (* copied from Help page *)

(* this plot works *)
DiscretePlot[Evaluate@CDF[\[ScriptCapitalD], x], {x, 0, 8}, 
 ExtentSize -> Left]

RandomVariate[ \[ScriptCapitalD  ]

I at least get a "not implemented message". Oh dear.

I tried using the partial sum to k, say, (1-2^(-1-k)) and then ProbabilityDistribution[ "CDF", 1-2^(-1-k), {k, 0, inf, 1} ] but this does not even give a valid ProbabilityDistribution[] object.

Cheers

Barrie

>>> On 16/12/2010 at 9:48 pm, in message <201012161048.FAA11797 at smc.vnet.net>,
omri-piano <omrit1248 at gmail.com> wrote:
> Hi,
> I would like to define a statistical distribution of my own. I would like to 
> sample from it, as when sampling from one of the standard Mathematica 
> distributions, like RandomInteger[BinomialDistribution[n,p]].
> 
> The pdf of my distribution should look like:
> 
> MyDistribution [j_, p_, n_]:=Binomial[n,(n*j)]*p^(n*j)*(1-p)^(n-n*j)
> 
> Is that possible?
> Thanks,
> Omri.



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