I am trying to assign scores for URLs based on their view counts. I have about 300,000 URLs. In a two-day interval,
- only 1 URL got more than 5000 views
- 8 got between 1,000 and 5,000 views
- about 500 got between 100 and 1,000 views
- about 7,000 got between 10 and 100 views
- about 18,000 got between 1 and 10 views
- the rest got no views
I want to find a function which gives scores of less than 0.1 for 1 to 10 views and grow quickly from 0.1 and reach about 0.75 for 100 views and then gradually increase to 1.0 for the URL with maximum views. I believe my goal is to find an "S-curve" function in a log-linear plot. I am not too strict about the $y$-values themselves.
I tried the 2D function finder tool at zunzun, and it gives a function like $y = ax^b / (c^b + x^b) + d$ but I am unable to figure out what values I should use for the constants $a$, $b$, $c$ and $d$.
UPDATE: Figured out how to get the values for the constants from zunzun (it gives a PDF if I click on "Go to this equation"), but the function with the constants in the PDF is not fitting those points! I tried fooplot.