Power Law:(18)Benfords Law

(2008/11/08)
DO図書館）：再読,Rereading
黄金比はすべてを美しくするか?―最も謎め... マリオ リヴィオ、Mario Livio、 斉藤 隆央 (単行本 - 2005/12)
p.286-290:Article on Benfords Law
The Golden Ratio /The Story of Phi, the World's Most Astonishing Number by Mario Livio

ベンフォードの法則を再び思い出す。
Benfords law is recalled again.
~~~
http://en.wikipedia.org/wiki/Benfords_law
d p
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%
~~~
べき乗傾向をチェック。
Power Law tendency is checked.

A,Bを求める。
A and B are obtained.

y = -0.8631x -1.1606
->
ln(y) = -0.8631*ln(x) -1.1606

LN
(x, y)=(1, exp(-1.1606)),(9, exp(-0.8631*ln(9) -1.1606)
=(1, 0.313),(9, 0.047)
Relative value)
=(1, 0.313/0.047),(9, 1)
=(1, 6.66),(9, 1)
A=-0.863
B=6.66

~~~
http://humanbeing-etcman.blogspot.com/2008/11/power-law11graph-structure-in-web.html
Power Law:(11)のデータに、追加。
It adds it to the data of Power Law:(11).

"A","B","memo","Category"
-0.863,6.66,"Power Law:(18),Benfords Law",unknown...

powerlaw-11-a-b.txt + (this data) = powerlaw-18-a-b.txt

~~~
Rでplotする。
Plot is done by R.
:リュカ数の場合,in case of Lucas number

data_ab = read.csv("powerlaw-18-a-b.txt");
plot(log(abs(data_ab$A)), log(data_ab$B), xlab="log(abs(a))", ylab="log(b)", xlim=c(-2, 2), ylim=c(1, 15), col="orange", pch=20, main="Scatter chart:a-b, Power Law(18) with Lucas")
abline(log(11), log(exp(5)), col="gray", lty=2)
abline(log(18), log(exp(5)), col="gray", lty=2)
abline(log(29), log(exp(5)), col="gray", lty=2)
abline(log(47), log(exp(5)), col="gray", lty=2)
abline(log(76), log(exp(5)), col="gray", lty=2)
abline(log(123), log(exp(5)), col="gray", lty=2)
abline(log(322), log(exp(5)), col="gray", lty=2)
abline(log(843), log(exp(5)), col="gray", lty=2)
abline(log(5778), log(exp(5)), col="gray", lty=2)
abline(log(9349), log(exp(5)), col="gray", lty=2)
abline(log(24476), log(exp(5)), col="gray", lty=2)
abline(log(39603), log(exp(5)), col="gray", lty=2)
abline(log(167761), log(exp(5)), col="gray", lty=2)
abline(log(271443), log(exp(5)), col="gray", lty=2)
abline(v = log(1), col="red")



今回追加したデータは、Lucas(n=5,11)のラインに引っかかっている。
The data added this time is caught to the line of Lucas(n=5,11).
~~~
end