Revamp our negative binomial explanation (#5300)

[herve-91]

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[michaelosthege]

@ColCarroll does this look good from the math side?

[ericmjl]

Having used the NB distribution in multiple places, I can confirm that the explanation is correct. Though, I'm not @ColCarroll and not a mathematician either, I will defer to @ColCarroll!

[codecov]

Codecov Report

Merging #5365 (02043e3) into main (d52655d) will increase coverage by 3.08%.
The diff coverage is n/a.

@@            Coverage Diff             @@
##             main    #5365      +/-   ##
==========================================
+ Coverage   80.36%   83.45%   +3.08%     
==========================================
  Files          89      132      +43     
  Lines       14808    26070   +11262     
==========================================
+ Hits        11901    21757    +9856     
- Misses       2907     4313    +1406     

Impacted Files	Coverage Δ
pymc/distributions/discrete.py	98.77% <ø> (ø)
pymc/parallel_sampling.py	86.71% <0.00%> (-1.00%)	⬇️
pymc/distributions/continuous.py	96.93% <0.00%> (-0.50%)	⬇️
pymc/step_methods/metropolis.py	82.97% <0.00%> (-0.08%)	⬇️
pymc/distributions/__init__.py	100.00% <0.00%> (ø)
pymc/distributions/distribution.py	91.40% <0.00%> (ø)
pymc/tests/test_variational_inference.py	0.00% <0.00%> (ø)
pymc/tests/test_tuning.py	96.42% <0.00%> (ø)
pymc/tests/test_posteriors.py	100.00% <0.00%> (ø)
pymc/tests/test_data_container.py	99.53% <0.00%> (ø)
... and 43 more