# `mode` and `modes` fail in Distributions.jl

The `Distributions.jl` package does not calculate correctly the theoretical mode and/or modes under models like `Binomial`, `Poisson` and `NegativeBinomial` here some examples:

``````using Distributions

## Example 1
B = Binomial(3, 0.5)
v = collect(0:3);
hcat(v, pdf.(B, v)) # theoretical modes are 1 and 2
pdf(B, 1) == pdf(B, 2) # true, as expected
modes(B) # should return 1 and 2 not just 2
mode(B) # should return 1 not 2
# But surprisingly:
D = DiscreteNonParametric(v, pdf.(B, v))
pdf(D, 1) == pdf(D, 2) # true, as expected
modes(D) # 1 and 2, as expected
mode(D) # 1, as expected

## Example 2
P = Poisson(2.0)
x = collect(0:4);
hcat(x, pdf.(P, x)) # theoretical modes are 1 and 2
pdf(P, 1) == pdf(P, 2) # true, as expected
modes(P) # 1 and 2, as expected
mode(P) # should return 1 not 2

## Example 3
N = NegativeBinomial(3, 0.5)
y = collect(0:3);
hcat(y, pdf.(N, y)) # theoretical modes are 1 and 2
pdf(N, 1) == pdf(N, 2) # should be true
pdf(N, 1) - pdf(N, 2) # very small positive difference
pdf(N, 1) > pdf(N, 2) # so numerically the mode should be 1 but:
mode(N) # oops! 2 instead of 1
modes(N) # should return 1 and 2 not just 2
``````

This is indeed an error. It falls back to a generic method because no method for `modes` is defined for `NegativeBinomial`. I can submit an issue if you do not have a github account.

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Ok then, I have just submitted the issue. Thanks.

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I am cross-referencing the issue in case someone comes across this thread.

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