Allow sampling NegativeBinomial for p==1 (#1575)

* Allow sampling `NegativeBinomial` for `p==1`

* Draw multiple samples

Co-authored-by: David Widmann <devmotion@users.noreply.github.com>

Co-authored-by: David Widmann <devmotion@users.noreply.github.com>

Author: simsurace

src/univariate/discrete/negativebinomial.jl

@@ -118,7 +118,13 @@ invlogcdf(d::NegativeBinomial, lq::Real) = convert(Int, nbinominvlogcdf(d.r, d.p
 invlogccdf(d::NegativeBinomial, lq::Real) = convert(Int, nbinominvlogccdf(d.r, d.p, lq))
 
 ## sampling
-rand(rng::AbstractRNG, d::NegativeBinomial) = rand(rng, Poisson(rand(rng, Gamma(d.r, (1 - d.p)/d.p))))
+function rand(rng::AbstractRNG, d::NegativeBinomial)
+    if isone(d.p)
+        return 0
+    else
+        return rand(rng, Poisson(rand(rng, Gamma(d.r, (1 - d.p)/d.p))))
+    end
+end
 
 function mgf(d::NegativeBinomial, t::Real)
     r, p = params(d)

test/negativebinomial.jl

@@ -17,4 +17,5 @@ end
 @testset "Check the corner case p==1" begin
     @test logpdf(NegativeBinomial(0.5, 1.0), 0) === 0.0
     @test logpdf(NegativeBinomial(0.5, 1.0), 1) === -Inf
+    @test all(iszero, rand(NegativeBinomial(rand(), 1.0), 10))
 end