correlation among random numbers
- To: mathgroup at smc.vnet.net
- Subject: [mg41103] correlation among random numbers
- From: Andrea Romanino <andrea.romanino at cern.ch>
- Date: Sat, 3 May 2003 03:27:08 -0400 (EDT)
- Organization: CERN
- Sender: owner-wri-mathgroup at wolfram.com
A Mathematica program I wrote that uses a Montecarlo method to generate
a probability distribution gives incorrect results.
The problem turns out to be due to an unexpected correlation among
independent random variables. In its simplest form, the problem is
illustrated in the notebook you can find attached.
I am using Mathematica 4.2.0 for Linux. The problem also arises with the
version 4.1.
While I can easily get rid of that correlation with "empirical"
modifications to the program, I am afraid that other correlations, not
leading to obviously incorrect results, may be hidden in the results. I
would therefore be extremely grateful if anyone could help me
understanding the origin of the problem and how to avoid it.
Thank you very much,
Andrea Romanino
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"Correlation between independent random numbers (",
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Cell["\<\
Omitting one of the random number generations between r and x or \
between x and y destroys the correlation.
Same if Random[NormalDistribution[0,1]] is replaced by Random[]\
\>", \
"Subsection"],
Cell["\<\
To see that the correlation indeed arises evaluate the cells below
The correlation arises between the variables r, x and y in the form Mod[x-y, \
1] - r = 0
Omitting one of the random number generations between r and x (or between x \
and y) eliminates the correlation
Idem if one of the \"Random[NormalDistribution[0,1]]\" is replaced by \
\"Random[]\" or viceversa\
\>", "Subsection"],
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\(\(nrnd = 10;\)\), "\n",
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Do[\[IndentingNewLine]r = Random[]; \[IndentingNewLine]Random[
NormalDistribution[0, 1]]; \[IndentingNewLine]Random[
NormalDistribution[0, 1]]; \[IndentingNewLine]Random[
NormalDistribution[0, 1]]; \[IndentingNewLine]Random[
NormalDistribution[0, 1]]; \[IndentingNewLine]Random[
NormalDistribution[0, 1]]; \[IndentingNewLine]Random[
NormalDistribution[0, 1]]; \[IndentingNewLine]Random[
NormalDistribution[0, 1]]; \[IndentingNewLine]Random[
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\[IndentingNewLine]Random[]; \[IndentingNewLine]x =
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\[IndentingNewLine]Random[]; \[IndentingNewLine]y =
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NormalDistribution[0, 1]]; \[IndentingNewLine]Random[
NormalDistribution[0, 1]]; \[IndentingNewLine]Random[
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NormalDistribution[0, 1]]; \[IndentingNewLine]Random[
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\[IndentingNewLine]Random[]; \[IndentingNewLine]x =
Random[]; \[IndentingNewLine]Random[]; \[IndentingNewLine]Random[]; \
\[IndentingNewLine]Random[]; \[IndentingNewLine]y =
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nrnd}];\), "\[IndentingNewLine]",
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What one should obtain (I have just removed one line from the cell \
above)\
\>", "Subsection"],
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NormalDistribution[0, 1]]; \[IndentingNewLine]Random[
NormalDistribution[0, 1]]; \[IndentingNewLine]Random[
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\[IndentingNewLine]Random[]; \[IndentingNewLine]y =
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