20170724, 12:24  #1 
Sep 2011
3×19 Posts 
Inverse of Smoothness Probability
The probability that a random number below X is Bsmooth is given by u^{u}, where u=ln(X)/ln(B). However, I would like the do the inverse, that is, given the smoothness probability and B, how do I solve for X?
I have a solution via Newton method. Is there a closed form? 
20170724, 19:53  #2  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
24D2_{16} Posts 
Quote:


20170725, 09:10  #3  
Sep 2011
3·19 Posts 
Quote:


20170725, 10:07  #4  
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 
Quote:
The links he provides are sources for p ≈ some_better_function_of(X, B). Find those better functions before trying to invert them. 

20170725, 10:21  #5  
Sep 2011
3·19 Posts 
Quote:


20170725, 16:33  #6  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·3·1,571 Posts 
Incidentally, I have just heard from much more knowledgeable people, and I will simply quote:
Quote:


20170725, 16:41  #7 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
22322_{8} Posts 
And for the Inverse of Smoothness Probability question, you want a reasonable numerical estimate the inverse of Dickman function.
So you want to take Newton method on the inverse of Dickman ρ  because if you know the derivative of Dickman ρ by definition, then you know the derivative of the inverse of Dickman ρ. 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
mi64: inverse does not exist  wreck  NFS@Home  1  20160508 15:44 
Quick smoothness test  Sam Kennedy  Programming  18  20130121 14:23 
Lurid Obsession with Mod Inverse  only_human  Miscellaneous Math  26  20120810 02:47 
Inverse of functions  Raman  Math  5  20110413 23:29 
Smoothness test  Washuu  Math  12  20050627 12:19 