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Benford's law


Dirtyhip
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Baloney, or valid mathematical theory?

Seems like bullshit.  I looked at the numbers on the stocks today:

Dow 27,386.98 185.46 0.68%  
  S&P 500 3,349.16 21.39 0.64%  
  Nasdaq 11,108.07 109.67 1.00%  
  GlobalDow 3,001.06 -2.58 -0.09%  
  Gold 2,074.30 25.00 1.22%  
  Oil 42.00 -0.19 -0.45

 

Does not correlate to the theory.

Discus. 

 

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All the leading numbers are less than 5.

Of the 18 numbers shown, 6 (30%) of the leading significant numbers are 1 which is consistent with the prediction.

Benfords Law is about the statistical probability of some event happening so there is always the chance that you get a set of data that does not correlate with the prediction.  That doesn't invalidate the "law".

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9 hours ago, Mr. Grumpy said:

All the leading numbers are less than 5.

Of the 18 numbers shown, 6 (30%) of the leading significant numbers are 1 which is consistent with the prediction.

Benfords Law is about the statistical probability of some event happening so there is always the chance that you get a set of data that does not correlate with the prediction.  That doesn't invalidate the "law".

Is that how the weather people predict the weather? 

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  • 2 weeks later...
On 8/6/2020 at 3:27 PM, Dirtyhip said:

Seems like bullshit.  I looked at the numbers on the stocks today:

I guess I can stop reading today...  I learned something new.     

I found this... Yeah my brain understands Excel (too many years of work)   https://www.journalofaccountancy.com/issues/2017/apr/excel-and-benfords-law-to-detect-fraud.html

The larger the better. Benford's Law works better with larger sets of data. While the law has been shown to hold true for data sets containing as few as 50 to 100 numbers, some experts believe data sets of 500 or more numbers are better suited for this type of analysis.

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I had never heard of Benford's Law before, but a quick Google and Wikipedia explanation makes some sense: "The law states that in many naturally occurring collections of numbers, the leading significant digit is likely to be small."

The "law" (it's actually a "limited theorem") tends to work when there are several significant figures (measured digits).  If you only have units, there is one 1, one 2, one 3, etc.  But when you hit the 10's you have ten 1's before ten 2's before ten 3's etc.  By the time you get to the 1000's, there are 1000 1's before 1000 2's etc.

So for all of the first 2000 whole numbers, there are 1111 that begin with 1!

Numbers that grow to more than a couple digits are going to pass through the large percentage beginning with 1's, then 2's then 3's before they get to the higher numbers.

Of course, they have to grow through the 7's, 8's, and 9's before they get to the next set of 1's, but they'll always have to spend at least as much time growing in the 1's as any higher number.

It's not completely intuitive, but it makes some sense.

 

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