remove psignrank from Rmath

[ArnoStrouwen]

This PR attempts to reimplement psignrank in pure Julia, to get rid of any GNU license issues with the R version @andreasnoack .
The Rmath version returns the exact correct decimal number, while my version has some slight floating point error.
I'm not sure why this is because, the Rmath version also containts floating point operations:
https://github.com/JuliaStats/Rmath-julia/blob/6f2d37ff112914d65559bc3e0035b325c11cf361/src/signrank.c#L161

julia> @btime HypothesisTests.psignrank.(0:sum(0:n), n, true)
  1.030 μs (38 allocations: 5.41 KiB)
11-element Vector{Float64}:
 0.0625
 0.12500000000000003
 0.18750000000000003
 0.3125
 0.4375
 0.5625000000000001
 0.6875000000000001
 0.8125000000000001
 0.8749999999999999
 0.9375000000000001
 1.0
 
 julia> @btime Rmath.psignrank.(0:sum(0:n), n, true)
  1.950 μs (5 allocations: 256 bytes)
11-element Vector{Float64}:
 0.0625
 0.125
 0.1875
 0.3125
 0.4375
 0.5625
 0.6875
 0.8125
 0.875
 0.9375
 1.0


julia> @btime HypothesisTests.psignrank.(0:sum(0:n), n, false)
  1.130 μs (38 allocations: 5.41 KiB)
11-element Vector{Float64}:
 1.0
 0.9375000000000001
 0.8749999999999999
 0.8125000000000001
 0.6875000000000001
 0.5625000000000001
 0.4375
 0.3125
 0.18750000000000003
 0.12500000000000003
 0.0625


julia> @btime Rmath.psignrank.((0:sum(0:n)).-1, n, false)
  1.960 μs (6 allocations: 288 bytes)
11-element Vector{Float64}:
 1.0
 0.9375
 0.875
 0.8125
 0.6875
 0.5625
 0.4375
 0.3125
 0.1875
 0.125
 0.0625

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 80.00000% with 4 lines in your changes missing coverage. Please review.

Project coverage is 93.49%. Comparing base (1cbeccd) to head (739d3b5).

Files with missing lines	Patch %	Lines
src/wilcoxon.jl	80.00%	4 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #330      +/-   ##
==========================================
- Coverage   94.04%   93.49%   -0.55%     
==========================================
  Files          29       29              
  Lines        1814     1830      +16     
==========================================
+ Hits         1706     1711       +5     
- Misses        108      119      +11     

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[ArnoStrouwen]

Julia 1.3 complains about the use of begin, working around would be not too difficult, or we can up the CI bound to something more modern?

[devmotion]

I wonder if the function should be added to StatsFuns, to make it easier and to reduce dependencies in case you want to use it in some other package and since it's currently the main package with Julia implementations of Rmath functions.

[devmotion]

Is it actually possible to construct a Vector with non-Int length? I assume this could just always be an Int as it doesn't have any ilpact on the calculated values.

[ArnoStrouwen]

I wonder if the function should be added to StatsFuns, to make it easier and to reduce dependencies in case you want to use it in some other package and since it's currently the main package with Julia implementations of Rmath functions.

It should really go to Distributions, since this is calculating the null distribution, but I'm too lazy to implement all the other functions. I would leave it here for now and create an issue for upstreaming proper Wilcoxon related distributions.

[ArnoStrouwen]

Not bad:

julia> n = 4
       @btime HypothesisTests.psignrank.(0:sum(0:n), n, true)
  401.493 ns (25 allocations: 1.08 KiB)
11-element Vector{Float64}:
 0.0625
 0.125
 0.1875
 0.3125
 0.4375
 0.5625
 0.6875
 0.8125
 0.875
 0.9375
 1.0

julia> @btime HypothesisTests.psignrank.(0:sum(0:n), n, false)
  422.111 ns (25 allocations: 1.08 KiB)
11-element Vector{Float64}:
 1.0
 0.9375
 0.875
 0.8125
 0.6875
 0.5625
 0.4375
 0.3125
 0.1875
 0.125
 0.0625