Corrected rank normal distribution

[magneticflux-]

This does NOT fix #455 completely, but it corrects the normal distribution function to something that is known to be correct.

In the future, I plan to replace the normal CDF with a power law CDF, which is made easier by migrating the existing normal CDF to a math library right now.

[vercel]

@magneticflux- is attempting to deploy a commit to the github readme stats Team on Vercel.

A member of the Team first needs to authorize it.

[codecov]

Codecov Report

Merging #817 (c36810a) into master (dff732a) will decrease coverage by 0.06%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master     #817      +/-   ##
==========================================
- Coverage   93.94%   93.88%   -0.07%     
==========================================
  Files          22       22              
  Lines         677      670       -7     
  Branches      188      187       -1     
==========================================
- Hits          636      629       -7     
  Misses         37       37              
  Partials        4        4              

Impacted Files	Coverage Δ
src/calculateRank.js	89.74% <100.00%> (-1.75%)	⬇️
src/cards/stats-card.js	100.00% <0.00%> (ø)

---

Continue to review full report at Codecov.

Legend - Click here to learn more
Δ = absolute <relative> (impact), ø = not affected, ? = missing data
Powered by Codecov. Last update dff732a...c36810a. Read the comment docs.

[anuraghazra]

Thanks for working on this @magneticflux-

Can you show/add more examples on how this change is effected the ranks? that would be nice too see and for further tweaking the values.

[magneticflux-]

This PR replaces the approximation of the error function (used to compute the normal CDF) with a more precise approximation that is accurate to at least 18 significant decimal digits over the domain of the function. The details of the new approximation can be found here: https://mathjs.org/docs/reference/functions/erf.html

In practical terms, this PR reduces error in calculating the normal CDF. It reduces error near the mean slightly (as seen in the changed test value), but it reduces error at the extremes more.

Some examples:

Input | 30, 25, 5
New   | 0.15865525393145707
Old   | 0.15865526383236372

Input | 30, 25, 1.4241
New   | 0.12651182223941376
Old   | 0.12651187738346226

Again, this PR only addresses problem 1 that I bring up in #455. Problem 2, using an ill-suited probability distribution, is still an issue and I intend to open another PR that migrates to a different distribution (using the Math.js library I introduce in this PR).

[stale]

This issue has been automatically marked as stale because it has not had recent activity. It will be closed if no further activity occurs. Thank you for your contributions.

[magneticflux-]

To fix #455 completely, I'd like to log anonymous statistics for requests to the API so that we can create a histogram plot of their score. That would let us calculate a grade based on the average of all github-readme-stats users. Additionally, we could take a random sample of GitHub profiles to calculate and use that if we want to grade based on the average of all GitHub users. That would let us validate the assumption that the score follows a power-law distribution.

[stale]

This issue has been automatically marked as stale because it has not had recent activity. It will be closed if no further activity occurs. Thank you for your contributions.