User:Lord Matt/madness

Some Fun with assumed distributions - ignore me

$f(x)=\sum _{n=0}^{x-1}2^{n}$

let B = Number of Indexed Backlinks

$f(x)\approx {\sqrt {Backlinks}}$

${\sqrt {Backlinks}}\approx \sum _{n=0}^{PR-1}2^{n}$

My PR Factor Function M $M(x,B)={\frac {\sqrt[{4}]{B}}{x}}$

Exact PR Point function g $g(x)={\sqrt {\frac {f(x)}{x}}}$

Logarythmic distence to next g(x+1)

$D(x)=g(x+1)-g(x)$

long hand $D(x)=g(x+1)-g(x)={\sqrt {\frac {f(x+1)}{x+1}}}-{\sqrt {\frac {f(x)}{x}}}$

Estimated Percentage of the distence to the next level

${\frac {D(Pagerank)}{M(Pagerank,Backlinks)}}*100$

Full Math

${\frac {{\sqrt {\frac {f(Pagerank+1)}{Pagerank+1}}}-{\sqrt {\frac {f(Pagerank)}{Pagerank}}}}{\frac {\sqrt[{4}]{Backlinks}}{Pagerank}}}*100$

\sum_{0}^ {PR} 2^n

${\frac {{\sqrt {\frac {\sum _{n=0}^{PR}2^{n}}{Pagerank+1}}}-{\sqrt {\frac {\sum _{n=0}^{PR-1}2^{n}}{Pagerank}}}}{\frac {\sqrt[{4}]{Backlinks}}{Pagerank}}}*100$

$g(x)={\sqrt {\frac {f(x)}{PR}}}$

${\sqrt {\frac {f(PR)}{PR}}}-{\frac {\sqrt[{4}]{Backlinks}}{PR}}$

(1 - (4th root of B) / PR)

square root(15 + 16) / 5 = 1.11355287
(4th root of 237) / 4    = 0.980905332
 square root(15) / 4     = 0.968245837
(4th root of 237) / 5    = 0.784724265

\left = a_0 + a_1 (x-c) + a_2 (x-c)^2 + a_3 (x-c)^3 + \cdots