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> 2. Probability of a transaction resulting in value v is uniform from [0,99]. Totally false: http://en.wikipedia.org/wiki/Benford%27s_law http://en.wikipedia

by tjic 17y ago

> 2. Probability of a transaction resulting in value v is uniform from [0,99]. Totally false: http://en.wikipedia.org/wiki/Benford%27s_law http://en.wikipedia.org/wiki/Benford%27s_law Benford's law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way.

DarkShikari 17y ago
But this is change in a larger transaction, not the first digit. Past the first digit, Benford's Law still applies, but the effect becomes extremely tiny as one adds more digits to the front.
rfurmani 17y ago
This does not apply here since we are looking at the last digits, and not the first, so different rules apply. The bigger your price is, the more uniform the cents will be (aside from psychological factors like: 00, 95, 99 being very common)
mitko 17y ago
Benford's law is about the first digit of the number, it has nothing to do with the current problem. The pennies are the two last digits. However, IMO the assumption you quoted is indeed false but due to other reason: In real life, prices are not uniformly distributed because usually they are rounded to multiple of 5 cents or commonly they are .99 or .89 or s.th. like that. I am wondering what happens if we put non-uniform prior on the probability of the pennies. Another flaw in this research is forgeting that we often are getting change back. So maybe problem is to find combination not only to give exactly money, but giving and receiving change back. For example: Using 1,5,10,20,50 you can make exact 4c only by 1,1,1,1, (4 coins). But getting change you can do 5, -1 (2 coins).
- noodle 17y ago
  while i agree with the premise that the prices aren't uniformly distributed, i think its less of an issue than people think. there are undoubtedly uneven humps that favor certain areas. but i think that the actual result of real life retail transactions is a more level curve than you would expect due to things like multiple, varied item purchases and the possible inclusion of various types of sales tax.
Perceval 17y ago
Given the number of retailers that end prices in 9 or 5, one could probably calculate a better model of efficiency based on real world distributions. The secondary problem would be that tax is applied after the nominal price, and local taxes vary considerably.
graywh 17y ago
He didn't say it was true. > with the following stipulations:

by tjic 17y ago

DarkShikari 17y ago

But this is change in a larger transaction, not the first digit. Past the first digit, Benford's Law still applies, but the effect becomes extremely tiny as one adds more digits to the front.

rfurmani 17y ago

This does not apply here since we are looking at the last digits, and not the first, so different rules apply. The bigger your price is, the more uniform the cents will be (aside from psychological factors like: 00, 95, 99 being very common)

mitko 17y ago

Benford's law is about the first digit of the number, it has nothing to do with the current problem. The pennies are the two last digits. However, IMO the assumption you quoted is indeed false but due to other reason: In real life, prices are not uniformly distributed because usually they are rounded to multiple of 5 cents or commonly they are .99 or .89 or s.th. like that. I am wondering what happens if we put non-uniform prior on the probability of the pennies. Another flaw in this research is forgeting that we often are getting change back. So maybe problem is to find combination not only to give exactly money, but giving and receiving change back. For example: Using 1,5,10,20,50 you can make exact 4c only by 1,1,1,1, (4 coins). But getting change you can do 5, -1 (2 coins).

noodle 17y ago
while i agree with the premise that the prices aren't uniformly distributed, i think its less of an issue than people think. there are undoubtedly uneven humps that favor certain areas. but i think that the actual result of real life retail transactions is a more level curve than you would expect due to things like multiple, varied item purchases and the possible inclusion of various types of sales tax.

Perceval 17y ago

Given the number of retailers that end prices in 9 or 5, one could probably calculate a better model of efficiency based on real world distributions. The secondary problem would be that tax is applied after the nominal price, and local taxes vary considerably.

graywh 17y ago

He didn't say it was true. > with the following stipulations: