consistently treat Bernoulli as a distribution on Bools

[aplavin]

Currently, it's quite inconsistent: eg, eltype === Bool, rand()::Bool, minimum()::Bool, but mode and median are Int, and quantile is T (often, float).
With this PR Bernoulli returns Bool whenever possible and makes sense.

This is both self-consistent between functions on Bernoulli, and also makes it consistent with other discrete distributions like Binomial / Categorical / DiscreteUniform / DiscreteNonParametric that return the minimal type (often Int) for their quantile and other functions.

[codecov-commenter]

Codecov Report

❌ Patch coverage is 75.00000% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.36%. Comparing base (7f59245) to head (53c3ea2).

Files with missing lines	Patch %	Lines
src/univariate/discrete/bernoulli.jl	71.42%	2 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #2022   +/-   ##
=======================================
  Coverage   86.36%   86.36%           
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  Files         146      146           
  Lines        8789     8789           
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  Hits         7591     7591           
  Misses       1198     1198           

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[devmotion]

Can you revert the changes to quantile and cquantile? The current API (probably historically based on Rmath) is to never error but to return NaN for invalid arguments. I think this should be changed, but that requires a more general change of the API of these functions: #1805

[aplavin]

reverting quantile implies also reverting median for consistency, and then basically we lose the point of this PR

any hope of #1805 in the foreseeable future?

[aplavin]

btw, quantile throws sometimes already:

julia> quantile(Bernoulli{Int}(1), 2)
ERROR: InexactError: Int64(NaN)

[devmotion]

any hope of #1805 in the foreseeable future?

Has been ready since > 2 years, just needs a review.

reverting quantile implies also reverting median for consistency, and then basically we lose the point of this PR

The current implementation of quantile is wrong (IMO) but it's consistent. It would be worse if some distributions would behave differently, we can't start erroring just for Bernoulli. You can still change mode, modes and support without touching quantile/cquantile.

[aplavin]

we can't start erroring just for Bernoulli

It already errors sometimes (and with a different exception). In addition to the example above:

quantile(Bernoulli(1//3), 2)

[aplavin]

Any references to that? Where do you get that "The current API is to return NaN for invalid inputs"?

Currently, the situation is that basically all discrete distributions return integers from quantile. And naturally, they throw an exception when p not in 0..1.
Documentation doesn't seem to contradict this in the slightest.
Even Bernoulli often behaves like that. It is Bernoulli{Float}() that is an exception (resolved by this PR).

[nalimilan]

As I just noted at #1805, NaN is allowed for many continuous distributions (Normal, Geometric, Exponential, Cauchy, Bernoulli...). And discrete distributions don't throw DomainErrors, they just get an error during calculations, without any indication that it's intentional. Let's get that PR merged.

[aplavin]

discrete distributions don't throw DomainErrors

Technically, this doesn't throw a DomainError indeed:

Distributions.jl/src/univariate/discrete/discretenonparametric.jl

Line 165 in b0ae395

0 <= q <= 1 || throw(DomainError())

But only because there's no zero-argument constructor for DomainError. Seems pretty much intentional :)

continuous distributions (<...>, Bernoulli...)

??

[nalimilan]

But only because there's no zero-argument constructor for DomainError. Seems pretty much intentional :)

I was referring to

julia> quantile(Binomial(10, 0.2), 2)
ERROR: InexactError: Int64(NaN)

Though the DomainError error is funny.

continuous distributions (<...>, Bernoulli...)

Sorry, I was talking only about the special case of passing NaN: quantile(Bernoulli(), NaN).

[aplavin]

julia> quantile(Binomial(10, 0.2), 2)
ERROR: InexactError: Int64(NaN)

It's an error still, just a less understandable one. If preferred, this PR can be changed into throwing the same one for Bernoulli, although I think DomainError is cleaner.

Anyway, from experience with this and my previous PR attempts to Distributions over the years, I find it super hard to add/change anything in this package. I had barely any success with that, in stark contrast to other Julia packages. So I'll stop here, and just hope that some improvements do happen at some point...