JuliaStats / Distributions.jl / 1450

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WIP: replace binomial(n,k) with beta equivalent for pdf(BetaBinomial) (#549)

* replace binomial(n,k) with gamma equivalent

extends pdf to work with n <= 170, whereas the binomial function only allowed pdf calculations up to n <= 66

* switched to beta from ratios of gammas

* flipped around equation to remove second division

recommended by @ararslan

* Update betabinomial.jl

* added test for large n beta binomial pdf calculation. asserts that new
pdf function works with n >= 1029, compared to n >= 66 possible when
using binomial(n,k)

* fix spacing

* updated pdf functions with inverse n choose k to avoid a rounding

* saving before checking current master for test accuracy

* added additional tests, restructured pdf functions to have more similar
syntax

* pre-allocate pdf(d) array to return, and swap a division for a
multiplication, which saves several µs

* remove static Float64 declaration in favor of dynamic type, add
inbounds, adjust spacing for style consistency

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