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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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