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Re: Random number generation( b/w two limits) with a gaussian

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109784] Re: Random number generation( b/w two limits) with a gaussian
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Mon, 17 May 2010 07:12:08 -0400 (EDT)

On 5/16/10 at 5:57 AM, elvisgraceland at gmail.com wrote:

>Dear experts, Is it possible to generate random numbers b/w any two
>limits (say b/w -4 & 4 ) which would comply to a gaussian
>distribution ?

No. By definition, the domain for a gaussian distribution
extends from -Infinity to +Infinity. Any distribution bounded to
the range of -4 to 4 cannot be gaussian. But, having said that,
it is possible to have a gaussian distribution that has a very
low likelihood of finding values outside the range of -4 to 4.

RandomReal[NormalDistribution[0, .5]]

The probability of finding a value outside of the range from -4
to 4 for this guassian distribution would be:

In[2]:= 1 - (CDF[NormalDistribution[0, .5], 4] -
    CDF[NormalDistribution[0, .5], -4])

Out[2]= 1.3322676295501878*^-15

The other choice would be to do

8(RandomReal[BetaDistribution[a,a]]-.5)

with a suitably large value for a

This distribution cannot have values outside the range of -4 to
4, is symmetrical and approaches the kurtosis of a normal
distribution as a tends to infinity



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