[jsweojtj]

I understand.

There is a distribution of leading digits that looks like:

    d   P(d)
    1   30.1%   
    2   17.6%   
    3   12.5%   
    4   9.7%    
    5   7.9%    
    6   6.7%    
    7   5.8%    
    8   5.1%    
    9   4.6%    
 

As wikipedia says, "It has been shown that this result applies to a wide variety of data sets, including electricity bills, street addresses, stock prices, house prices, population numbers, death rates, lengths of rivers, physical and mathematical constants."

Neat! For each of those data sets you get the same distribution. Now, someone (I won't say who), says that it also is true for the uniform distribution.

But it isn't.

It simply isn't.

And I said as much when I said, "The leading digits of a uniform distribution does not follow Benford's law."

And your counter example is if you take a uniform distribution from 0-300, the leading digits go to something like:

    d   P(d)
    1   36.7%   
    2   36.7%   
    3   3.7%   
    4   3.7%    
    5   3.7%
    6   3.7%    
    7   3.7%
    8   3.7%
    9   3.7%

Great, so I don't know how we can disagree at this point. The above distribution is not Benford's Law.

> "The leading digits of a uniform distribution does not follow Benford's law." -- me

And you, directly disagreeing with that correct statement:

> This just goes to show that we have to check our assumptions, as scientists or mathematicians trying to prove a statement. -- EGreg

Indeed.