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    bizarre distributions






    Perhaps some expert here can shine some light on the strange results I've been
    experiencing lately.

    I wanted to explore the idea of creating a secondary distribution from a chi square.
    My computer programs have a inner loop that begins with generating 320 random numbers between 0 and 15. X square is computed and if X > 24.996 (for the 0.05 case) a "hits" counter is incremented. This inner loop is repeated 4,000 times after which the # of hits is saved. For the .05 case, the expected mean is 4000 X .05 = 200. The outer loop consists of repeating the inner loop many hundreds of times to build a distribution. Outer loops I've called "tests".

    Results for 0.01 (mean = 40) and 0.05 (mean = 200) are shown in the image file.
    The 0.01 result doesn't appear to be terribly skewed but the "weights" are on the
    left side (decidedly more hits < mean than > mean). The 0.05 case is obviously
    skewed to the right.

    To eliminate the possibility that my pseudo random generator might be doing
    strange things, I was able to download over 100 megabytes of "quality" hardware
    generated random bytes. This was enough to do smaller sized tests which showed
    similar bizarre results. When I tried upping the initial number of random numbers
    from 320 to 640 both the 0.01 and 0.05 results were terribly right skewed.

    I had fully (and naively) expected to see normal distributions. In attempts to explore
    this further, I did programs for 4, 6 and 8 instead of the 16 random numbers
    mentioned above. All have similar strange results. Typically, 0.01 results were
    decidedly left skewed and 0.05 results are decidedly right skewed (but only
    when using 320 initial random #'s and not 640).

    I'm about to drop this whole thing since it's not going anywhere. But I am
    curious as to whether or not my results are mathematically predictable.

    Art
    Last edited by ArtK; 11-01-2014 at 12:18 PM.

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