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