Interesting "Laws"

[HungLikeJesus]

Stigler's Law of Eponymy

From Wikipedia:

Stigler's law of eponymy is a process proposed by University of Chicago statistics professor Stephen Stigler in his 1980 publication "Stigler’s law of eponymy." In its simplest and strongest form it says: "No scientific discovery is named after its original discoverer." Stigler named the sociologist Robert K. Merton as the discoverer of "Stigler's law", consciously making "Stigler's law" exemplify Stigler's law.

[HungLikeJesus]

Benford's Law
From Wikipedia:

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. According to this law, the first digit is 1 about 30% of the time, and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than 5% of the time. This distribution of first digits is the same as the widths of gridlines on the logarithmic scale.


This counter-intuitive result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature). It tends to be most accurate when values are distributed across multiple orders of magnitude.


The graph (below) shows Benford's law for base 10. There is a generalization of the law to numbers expressed in other bases (for example, base 16), and also a generalization to second digits and later digits.
It is named after physicist Frank Benford, who stated it in 1938, although it had been previously stated by Simon Newcomb in 1881.

[Lamplighter]

[quote=HungLikeJesus;780792]Benford's Law
From Wikipedia:

This counter-intuitive result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature). It tends to be most accurate when values are distributed across multiple orders of magnitude.

OK, pls explain to me why this is "counter-intuitive ?
and, what difference would it make if it was distributed across orders of magnitude.

If I am going to count anything, I start with "1". Therefore in a set of any size,
there will always be a larger number of "1's" than of "2's" than of "3's"...etc.
And to point out the obvious, in small sets, there may not even be a "9" or "0"

In the examples of the quote above,
a small town might have street addresses of 100's, 200's... to 700's, but no 800's or 900's. etc.

I guess I'm not getting Benford's idea of the whole thing.

[HungLikeJesus]

Originally Posted by HungLikeJesus

Benford's Law
From Wikipedia:

Hey, I just noticed that they left off consideration of the digit 0 (and the digit þ)

[Pete Zicato]

Here they are HLJ!

Half of all people are below average.

Kaa's Law: In any sufficiently large group of people most are idiots.

[ZenGum]

Originally Posted by HungLikeJesus

Hey, I just noticed that they left off consideration of the digit 0 (and the digit þ)

No number starts with a zero.

Or else they all do. 0001, 002, etc. We take the first significant figure.

What about 0.005, you ask?

5 x 10^-3

[BigV]

Originally Posted by ZenGum

No number starts with a zero.

Or else they all do. 0001, 002, etc. We take the first significant figure.

What about 0.005, you ask?

5 x 10^-3

orly? What about the product of

5 x 0 = ?

[tw]

Originally Posted by ZenGum

No number starts with a zero.

In computers, all positive numbers start with zero. Negative numbers start with one.

[Sundae]

Sod's Law.
It's like ten thousand spoons, when all you need is a knife.

[infinite monkey]

Hahhahaahaa...brother just sent me this today.

[Sundae]

Synchronicity!
It must mean something.

Probably being deluged by spoons.

[toranokaze]

A woman who writes a song called irony, but has no concept of the word; now that is ironic.

[HungLikeJesus]

Pareto principle
From Wikipedia:

The Pareto principle (also known as the 80–20 rule, the law of the vital few, and the principle of factor sparsity) states that, for many events, roughly 80% of the effects come from 20% of the causes.

Business-management consultant Joseph M. Juran suggested the principle and named it after Italian economist Vilfredo Pareto, who observed in 1906 that 80% of the land in Italy was owned by 20% of the population; he developed the principle by observing that 20% of the pea pods in his garden contained 80% of the peas.

It is a common rule of thumb in business; e.g., "80% of your sales come from 20% of your clients". Mathematically, where something is shared among a sufficiently large set of participants, there must be a number k between 50 and 100 such that "k% is taken by (100 − k)% of the participants". The number k may vary from 50 (in the case of equal distribution, i.e. 100% of the population have equal shares) to nearly 100 (when a tiny number of participants account for almost all of the resource). There is nothing special about the number 80% mathematically, but many real systems have k somewhere around this region of intermediate imbalance in distribution.

Due to the scale-invariant nature of the power law relationship, the relationship applies also to subsets of the income range. Even if we take the ten wealthiest individuals in the world, we see that the top three (Warren Buffett, Carlos Slim Helú, and Bill Gates) own as much as the next seven put together.
...
In the systems science discipline, Epstein and Axtell created an agent-based simulation model called SugarScape, from a decentralized modeling approach, based on individual behavior rules defined for each agent in the economy. Wealth distribution and Pareto's 80/20 Principle became emergent in their results, which suggests that the principle is a natural phenomenon.
…
In health care in the United States, it has been found that 20% of patients use 80% of health care resources.

Several criminology studies have found that 80% of crimes are committed by 20% of criminals.

[ZenGum]

85% of ....

You know the rest.

[HungLikeJesus]

As a real-world example, Lamp, let's say that we looked at the number of views for threads in one Cellar forum - Nothingland, for example. Would you expect the first digit to have a uniform distribution, or would you expect it to follow the distribution indicated by Benford's Law?