Irwin-Hall and Bates distributions

[jaksle]

These 2 distributions are nearly the same thing, I slightly generalised the definition from Wikipedia so that this IrwinHall encompasses both.

[Santymax98]

Hi, thank you so much for your contribution. I've finished the review and testing... overall, everything is perfect... could you correct or elaborate on that part so I can then integrate it into the main branch? It would only be for large-number security; everything else is OK.

[codecov-commenter]

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Codecov Report

❌ Patch coverage is 73.52941% with 27 lines in your changes missing coverage. Please review.
✅ Project coverage is 69.33%. Comparing base (360d427) to head (9b2d863).

Files with missing lines	Patch %	Lines
src/continuous/IrwinHall.jl	70.00%	27 Missing ⚠️
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Additional details and impacted files

@@            Coverage Diff             @@
##             main       #9      +/-   ##
==========================================
+ Coverage   69.24%   69.33%   +0.09%     
==========================================
  Files          34       35       +1     
  Lines        1967     2061      +94     
==========================================
+ Hits         1362     1429      +67     
- Misses        605      632      +27     

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[jaksle]

The changes all look good for me :) One small note is I used Roots.Bisection() because Newton method was not stable. Why I don't know, so I might be better to keep it as it is.

I doubt this distribution is of much practical importance, but SciPy has it, Julia should have it. It is a matter of pride ;)

[Santymax98]

I understand, perhaps you can use Brent? After this I'll adjust the stability of Lomax and we'll do the merge.

[jaksle]

I checked. Roots.Brent and Roots.A42 are stable. Compared to bisection, Brent is around 2x faster. A42 is around 4x faster.