# Normal and power law distributions

## Main Question or Discussion Point

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?