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RandomReal[] and sampling a distribution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg110552] RandomReal[] and sampling a distribution
  • From: John Stone <stone at geology.washington.edu>
  • Date: Fri, 25 Jun 2010 07:27:09 -0400 (EDT)

I hope this is a simple question (perhaps too simple for the 
archives, which I did search).  Thanks in advance for any help.

I am trying to use RandomReal[ ] to sample from bins of different 
widths that span the interval 0 - 1.  The bin widths represent the 
weights I'm assigning to a family of trial solutions in an 
optimization problem.  The aim is to sample the solutions in 
proportion to their weights using a uniform distribution of random 
numbers generated by RandomReal[ ].

For a simple example, however, suppose there are 10 equally weighted 
solutions.  My selection process would use some code that looks like:

weights = Table[0.1, {10}];
bins = Accumulate[weights];
Select[bins, (# >= RandomReal[] &)][[1]]

Assuming the result of RandomReal[ ] is uniformly distributed, I 
expected this to return 0.1 as frequently as it returns 0.5 or 1, but 
it seems to return a distribution of values peaked around 0.5 (and 
seldom returns 0.9 or 1).

Graphically, the following I think is equivalent, and gives me a 
peaked, not a flat distribution:

Histogram[
  Table[
   Select[{0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1},
     (# >= RandomReal[ ] &)][[1]],
   {1000}]
]

Shouldn't the procedure in my example generate a flat distribution? 
Or am I missing something really simple?

Thanks again if you can help me solve this.
-- 
John Stone
Department of Earth and Space Sciences
University of Washington                        Phone: + 1 206 221-6332
Box 351310,  70 Johnson Hall                    Lab:   + 1 206 221-6383
Seattle, WA, 98195-1310, USA                    Fax:   + 1 206 543-0489

Web page:  http://depts.washington.edu/cosmolab


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