add signrank distribution

[ArnoStrouwen]

Implementation of the signrank distribution.
The cdf is heavily optimized, since that is what is needed for the popular hypothesis test associated with this distribution.

The testing in this package seems quite involved, I could use some pointers on where to add the tests.

using StatsFuns
using Rmath

signrankpdf.(-2:12,4)
dsignrank.(-2:12,4,false)

signranklogpdf.(-2:12,4)
dsignrank.(-2:12,4,true)

signrankcdf.(-2:12,4)
psignrank.(-2:12,4,true,false)

signranklogcdf.(-2:12,4)
psignrank.(-2:12,4,true,true)

signrankccdf.(-2:12,4)
psignrank.(-2:12,4,false,false)

signranklogccdf.(-2:12,4)
psignrank.(-2:12,4,false,true)

signrankinvcdf.(-0.01:0.01:1.01,4)
qsignrank.(-0.01:0.01:1.01,4,true,false)
signrankinvcdf.(0.0624,4)
signrankinvcdf.(0.0625,4)
signrankinvcdf.(0.0626,4)
qsignrank.(0.0624,4,true,false)
qsignrank.(0.0625,4,true,false)
qsignrank.(0.0626,4,true,false)

signrankinvlogcdf.(log.(0.0:0.01:1.01),4)
qsignrank.(log.(0.0:0.01:1.01),4,true,true) # 0.0 does not match, is the R definition correct?
qsignrank.(log(0.0),4,true,true)
qsignrank.(0.0,4,true,false) 
signrankinvlogcdf.(log(0.0624),4)
signrankinvlogcdf.(log(0.0625),4)
signrankinvlogcdf.(log(0.0626),4)
qsignrank.(log(0.0624),4,true,true)
qsignrank.(log(0.0625),4,true,true)
qsignrank.(log(0.0626),4,true,true)


signrankinvccdf.(-0.01:0.01:1.01,4)
qsignrank.(-0.01:0.01:1.01,4,false,false) 
signrankinvccdf.(0.0624,4)
signrankinvccdf.(0.0625,4)
signrankinvccdf.(0.0626,4)
qsignrank.(0.0624,4,false,false)
qsignrank.(0.0625,4,false,false)
qsignrank.(0.0626,4,false,false)

signrankinvlogccdf.(log.(0.0:0.01:1.01),4)
qsignrank.(log.(0.0:0.01:1.01),4,false,true) # 0.0 does not match
signrankinvlogccdf.(log(0.0624),4)
signrankinvlogccdf.(log(0.0625),4)
signrankinvlogccdf.(log(0.0626),4)
qsignrank.(log(0.0624),4,false,true)
qsignrank.(log(0.0625),4,false,true)
qsignrank.(log(0.0626),4,false,true)

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 0% with 55 lines in your changes missing coverage. Please review.

Project coverage is 57.97%. Comparing base (8f50565) to head (e63bf83).

Files with missing lines	Patch %	Lines
src/distrs/signrank.jl	0.00%	55 Missing ⚠️

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Flag	BASE (8f50565)	HEAD (e63bf83)
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##           master     #173      +/-   ##
==========================================
- Coverage   62.99%   57.97%   -5.03%     
==========================================
  Files          14       15       +1     
  Lines         635      690      +55     
==========================================
  Hits          400      400              
- Misses        235      290      +55     

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[andreasnoack]

I'd try to add it to test/rmath.jl` similarly to

StatsFuns.jl/test/rmath.jl

Lines 233 to 241 in 8f50565

	rmathcomp_tests("chisq", [
	((1,), 0.0:0.1:8.0),
	((4,), 0.0:0.1:8.0),
	((9,), 0.0:0.1:8.0),
	((9,), 0:8),
	((1,), 0f0:0.1f0:8f0),
	((1,), Float16(0):Float16(0.1):Float16(8)),
	((9,), 0//1:8//1),
	])

to compare with the Rmath results.

[ArnoStrouwen]

Some differences with R remain:
How minus infinity is handled in invlogcdf, in my opinion is it correct to return zero here and not NaN.

julia> signrankinvcdf(4, 0.0)
0.0
julia> signrankinvlogcdf(4, log(0))
0.0
julia> qsignrank.(0.0,4,true,false) 
0.0
julia> qsignrank.(log(0.0),4,true,true)
NaN

Rounding in the quantiles is also an issue:

julia> qsignrank.(-2.1,4,true,true)
1.0
julia> qsignrank.(-2.0794415416798357,4,true,true)
1.0
julia> qsignrank.(-2.0,4,true,true)
2.0

julia> signrankinvlogcdf(4,-2.1)
1.0
julia> signrankinvlogcdf(4,-2.0794415416798357)
2.0
julia> signrankinvlogcdf(4,-2.0)
2.0

The true cdf jumps at 0.125, but that value does not roundtrip with exp/log.

julia> exp(-2.0794415416798357)
0.12500000000000003
julia> log(0.125)
-2.0794415416798357
julia> exp(log(0.125))
0.12500000000000003

[ArnoStrouwen]

I improved rounding by getting rid of all exp in my code.
Still, some rounding differences with R remain for invlogccdf, which I don't know how to solve.
https://github.com/JuliaStats/Rmath-julia/blob/6f2d37ff112914d65559bc3e0035b325c11cf361/src/dpq.h#L52-L53

[andreasnoack]

I think that you might be able to match for this one if you instead of relying on log1mexp then do a search similarly to signrankinvlogcdf.