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Fix mode(Binomial) and modes(Binomial) #1931

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Fix mode(Binomial) and modes(Binomial) #1931

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194adf9
Returns smallest `mode` in `mode(Binomial)`, fix `modes`
marcusps Dec 17, 2024
ea39724
Update tests for mode(Binomial) and modes(Binomial)
marcusps Dec 17, 2024
87df67f
Fix incorrect test
marcusps Dec 19, 2024
1116bf1
Add a few more tests
marcusps Dec 19, 2024
0fac6c0
Fix bug with mode calculation condition
marcusps Dec 19, 2024
6c0abd5
Merge branch 'master' into marcusps/fix-mode
marcusps Dec 19, 2024
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31 changes: 28 additions & 3 deletions src/univariate/discrete/binomial.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -67,11 +67,36 @@ params(d::Binomial) = (d.n, d.p)

mean(d::Binomial) = ntrials(d) * succprob(d)
var(d::Binomial) = ntrials(d) * succprob(d) * failprob(d)
function mode(d::Binomial{T}) where T<:Real

function mode(d::Binomial)
(n, p) = params(d)
v = (n + 1) * p
quasi_mode = floor(Int, v)
if quasi_mode == v
if p == 1
n
else
quasi_mode-1
end
else
quasi_mode
end
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AFAICT alternatives with fewer branches would be

Suggested change
v = (n + 1) * p
quasi_mode = floor(Int, v)
if quasi_mode == v
if p == 1
n
else
quasi_mode-1
end
else
quasi_mode
end
iszero(p) ? 0 : ceil(Int, (n + 1) * p) - 1

or

Suggested change
v = (n + 1) * p
quasi_mode = floor(Int, v)
if quasi_mode == v
if p == 1
n
else
quasi_mode-1
end
else
quasi_mode
end
max(0, ceil(Int, (n + 1) * p) - 1)

or

Suggested change
v = (n + 1) * p
quasi_mode = floor(Int, v)
if quasi_mode == v
if p == 1
n
else
quasi_mode-1
end
else
quasi_mode
end
clamp(ceil(Int, (n + 1) * p) - 1, 0, n)

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There is little to no difference in runtime between these options (or the option in the PR). The main difference is in the max runtime, and the PR options and the max(0, ceil(...)) have the shorter max runtime (the two are nearly identical with a max of about 10x the average runtime), while the max runtime for the other two options is about twice as long (about 20x the average runtime). The standard deviations show a similar pattern (but they are smaller than the average runtime).

Given there isn't much of a different in run times, I propose the PR version is preferable because it is easiest to read and reason about.

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@devmotion Is there another reason to consider fewer branches other than runtime?

end

function modes(d::Binomial)
(n, p) = params(d)
n > 0 ? floor(Int, (n + 1) * d.p) : zero(T)
v = (n + 1) * p
quasi_mode = floor(Int, v)
if quasi_mode == v
if p == 1
Int[n]
else
Int[quasi_mode-1, quasi_mode]
end
else
Int[quasi_mode]
end
end
modes(d::Binomial) = Int[mode(d)]

function skewness(d::Binomial)
n, p1 = params(d)
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15 changes: 11 additions & 4 deletions test/univariate/discrete/binomial.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -32,11 +32,18 @@ end
@test median(Binomial(45,3//10)) == 13
@test median(Binomial(65,3//10)) == 19
@test median(Binomial(85,3//10)) == 25

# Test mode
@test Distributions.mode(Binomial(100, 0.4)) == 40
@test Distributions.mode(Binomial(1, 0.51)) == 1
@test Distributions.mode(Binomial(1, 0.49)) == 0
@test mode(Binomial(100, 0.4)) == 40
@test mode(Binomial(1, 0.51)) == 1
@test mode(Binomial(1, 0.49)) == 0
@test mode(Binomial(4, 2//3)) == 3
@test mode(Binomial(6, 2//7)) == 1
@test mode(Binomial(7, 1//8)) == 0

@test modes(Binomial(4, 2//3)) == [3, 4]
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@test modes(Binomial(6, 2//7)) == [1, 2]
@test modes(Binomial(7, 1//8)) == [0, 1]

@test isplatykurtic(Bernoulli(0.5))
@test ismesokurtic(Normal(0.0, 1.0))
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