Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Normal and power law distributions

  1. Apr 29, 2008 #1
    Is it correct to say that independent random events (additively) lead to a normal distribution, and dependent random events (multiplicatively) lead to a power law distribution?

    The following might be trivial, but it was quite interesting to find for me, someone with a very limited knowledge of mathematics or statistics:

    Take a matrix of random numbers r(i,j), where 0 < r(i,j) < 1.

    Let S(i) = int( ( r(i,1) + r(i,2) +...+ r(i,j) )*n ), with S(i) >= S(i-1) if i >= i-1, that is, S is a sorted list of the integer parts of the sums of random numbers multiplied by an integer.

    Let P(i) = int( ( r(i,1) * r(i,2) * ... * r(i,j) )*n ), with P(i) >= P(i-1) if i >= i-1, that is P is a sorted list of the integer parts of the products of random numbers multiplied by an integer.

    Hypothesis (based simply on observation of graphs of S(i) and P(i)):

    the higher the values of i and j, the more S(i) approximates normal distribution, and P(i) approximates a power-law distribution.

    Is this right?
     
  2. jcsd
  3. Apr 29, 2008 #2
    Apologies, I meant the frequency of each S(i) or P(i).
    It may be better to describe what I did in the following way:
    I used a spreadsheet, and created a table, consisting of, say, 10,000 rows and 5 columns, of random numbers (using the spreadsheet's random number function). Then I added (or multiplied) the random numbers in each row. I multiplied the sums (or products) by, say, 100, and took the integer parts (to create "bins"). Then I sorted the "bins", calculated the frequency (number of occurencies in the list) of each "bin", and then put a graph on the frequency list. I hope this makes sense.
     
    Last edited: Apr 29, 2008
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Normal and power law distributions
  1. Normal Distributions (Replies: 4)

Loading...