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POnot random enough for monte carlo
 

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  1. POnot random enough for monte carlo
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    <p>I am trying to generate values from a normal distribution using a monte carlo method, as per the website <a href="http://math60082.blogspot.ca/2013/03/c-coding-random-numbers-and-monte-carlo.html" rel="nofollow">http://math60082.blogspot.ca/2013/03/c-coding-random-numbers-and-monte-carlo.html</a></p> <p>I modified the code a bit from the original so it calculates the variance and mean for the numbers generated directly to check if the method is working rather than do the tests separately (same difference really but just a heads up).</p> <p><strong>Question</strong></p> <p>Regardless of what I do, the variance is way above 1 and the mean is not zero. Is it possible the pseudo-random numbers generated aren't random enough?</p> <p><strong>Code</strong></p> <p><strong>PLEASE NOTE THAT THE AUTHOR OF THE ABOVE GIVEN WEBSITE IS THE PERSON WHO WROTE THE CODE</strong></p> <pre><code>#include &lt;cstdlib&gt; #include &lt;cmath&gt; #include &lt;ctime&gt; #include &lt;iostream&gt; using namespace std; // return a uniformly distributed random number double uniformRandom() { return ( (double)(rand()) + 1. )/( (double)(RAND_MAX) + 1. ); } // return a normally distributed random number double normalRandom() { double u1=uniformRandom(); double u2=uniformRandom(); return cos(8.*atan(1.)*u2)*sqrt(-2.*log(u1)); } int main() { double z; int N=1000; double array[N]; double mean=0 ,variance=0; srand(time(NULL)); for(int i=0;i&lt;N;i++) { z=normalRandom(); cout &lt;&lt; i &lt;&lt; "-&gt;"&lt;&lt; z&lt;&lt; endl; mean+=z; array[i]=z; } mean=mean/N ; cout &lt;&lt; " mean = " &lt;&lt; mean &lt;&lt; endl; for(int i=0;i&lt;N;i++) { variance = variance + (mean - array[i])*(mean - array[i]); } variance = variance/N; cout &lt;&lt; " variance = " &lt;&lt; variance &lt;&lt; endl; return 0; } </code></pre> <p><strong>UPDATE</strong></p> <p>Apparently as pointed by users, I screwed up and the program was not working because of a very silly mistake.</p>
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    1. COI've read in the past that generating a normal distribution random from a uniform random is generally not particularly accurate -- better to use a normal distribution RNG. (Dunno exactly where to find one, though. Used to be one in the old standard Fortran libs, but don't know about C++.)
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      1. USHot Licks
    2. CO@HotLicks: I don't know where you read that but that's a very shaky statement. Generation of normal distributions form a uniform distribution is quite a [common](http://en.wikipedia.org/wiki/Marsaglia_polar_method) [thing](http://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform). *However*, using a poor uniform generator (like `rand()`) will lead to a poor normal distribution.
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      1. USMike Bailey
    3. CO@HotLicks Noted, apparently the friend I am doing this for, wants it to be a monte carlo method.
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