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MathGroup Archive 2004

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Re: random numbers?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46161] Re: random numbers?
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Mon, 9 Feb 2004 05:54:09 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 2/7/04 at 11:35 PM, junk4 at microserf.org.uk (C Rose) wrote:

>I have already mentioned the Poisson distribution. This raises the
>question of what you mean by randomness. Really, what is meant is
>that the source of the random numbers follows a particular
>distribution (i.e. uniform distribution, Normal distribution,
>Poisson distribution, etc.). Once you have defined the distribution
>from which you want to sample, and have a method for generating
>number that follow that distribution, you need to be able to
>compare the two, to verify that your source is random enough. Here,
>one can use statistical tests.

While the above is true, it should be noted being able to generate random numbers from any given distribution is sufficient to generate numbers from any other distribution. This is because the cumulative distribution function for all distributions ranges from 0 to 1.

The most direct aplication of this observation is to generate numbers from a uniform distribution and use the inverse cumulative distribution function to transform uniformly distributed numbers to the desired distribution. 
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