multinomial sampling should rely on binomial

[YeungOnion]

addresses #183, but does not really fix it since binomial is naive sampling.

if we rely on binomial sampling then we can optimize once. This also updates the testing_boiler to work with Multinomial, notice how the tests are written to all use dynamically sized vectors and to rely on norms for approx absolute equality.

There is also a stoachastic test added, but I'm doubtful that I'm correct about both the test and sampling because it doesn't pass often enough. (Perhaps my choice of parameters in the test is not convergent enough to a normal distribution?) But a second pair of eyes on this would be helpful.

[codecov]

Codecov Report

Attention: Patch coverage is 57.93103% with 122 lines in your changes missing coverage. Please review.

Project coverage is 93.08%. Comparing base (993a4b5) to head (66b8d7e).
Report is 2 commits behind head on master.

Files with missing lines	Patch %	Lines
src/distribution/multinomial.rs	55.14%	122 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #287      +/-   ##
==========================================
- Coverage   93.73%   93.08%   -0.66%     
==========================================
  Files          53       53              
  Lines       12010    12196     +186     
==========================================
+ Hits        11258    11353      +95     
- Misses        752      843      +91     

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[YeungOnion]

perhaps I need test statistics to assess if the samples are likely from the distribution...

[FreezyLemon]

notice how the tests are written to all use dynamically sized vectors

Hm... the static types (i.e. SMatrix, SVector) have more type safety and so I generally agree that the dynamically sized types need more testing. But I'm not sure about just testing the dynamic types; we might miss problems with specific nalgebra code paths or even incorrect trait bounds that would exclude the static types from being used in the statrs API altogether.

Looking at #165, this would also exclude basically all multivariate tests from no_std environments without an allocator.

Not 100% sure the existing boiler macro can cover everything... the nalgebra-based distributions are a fair bit different after all. But I think that e.g. new_from_nalgebra should be preferred over just new since it works for both types of Matrix/vector.

[YeungOnion]

I agree we should be testing our API size generics and that tests should work on no_std if we have it. I'll revert that.

Do you have any other ideas to verify that samples are correctly generated?

[FreezyLemon]

Do you have any other ideas to verify that samples are correctly generated?

Not really, to be honest. Except for very rudimentary testing (samples are in the correct domain/range of values), you'd probably need to implement proper statistical test methods..

[YeungOnion]

I'll rely on other implementations of statistical tests and rv sampling to verify my implementation for now. Once we've got tests and verification for them, then I'll consider bootstrapping features.

[YeungOnion]

Tests use both static and dynamic allocators, but aren't broken out into separate tests, but they aren't interleaved into the test suite, so shouldn't be a big lift to conditionally compile them for a no_std option.

[YeungOnion]

Certainly not a thorough analysis, but it's safe to say the implementation is not likely correct.

>>> stats.cramervonmises_2samp(scipy_mnom_gen(), data) # scipy vs data
CramerVonMisesResult(statistic=[4.46216824 4.365037   4.57871893 4.39759045 4.64458355], pvalue=[4.92114127e-11 7.65537633e-11 3.194799
98e-11 6.57013333e-11
 2.73471246e-11])
>>> stats.cramervonmises_2samp(scipy_mnom_gen(), scipy_mnom_gen()) # scipy vs scipy
CramerVonMisesResult(statistic=[0.1209659  0.05345861 0.15851277 0.10590302 0.13809556], pvalue=[0.49155904 0.8550833  0.36467217 0.556
74849 0.42800996])

tested with n=1000, p=5*[0.2] where both scipy and statrs generated 10k samples