# What does \`density()\` do when applied to a \`Distribution\` directly?
**URL:** https://discourse.julialang.org/t/what-does-density-do-when-applied-to-a-distribution-directly/105621
**Category:** Visualization
**Tags:** plotting, plots, distributions, statsplots
**Created:** [October 31, 2023, 4:24pm UTC](https://discourse.julialang.org/t/what-does-density-do-when-applied-to-a-distribution-directly/105621 "2023-10-31T16:24:50Z")
**Posts on this page:** 7
**Page:** 1
### Author:  [@Alseidon](https://discourse.julialang.org/u/Alseidon)
#### Post date: [October 31, 2023, 4:24pm UTC](https://discourse.julialang.org/t/what-does-density-do-when-applied-to-a-distribution-directly/105621/1 "2023-10-31T16:24:50Z")
I just started experimenting with `Distributions.jl` and `StatsPlots.jl`, and made a basic mistake, writing `density(Normal())` instead of `density(rand(Normal(), 100_000))` or `plot(Normal())`. When executing
```julia
julia> plot(Normal(), label="plot()")
julia> density!(rand(Normal(), 100_000), label="density(rand())")
julia> density!(Normal(), label="density()")
```
Here is the result:
What is plotted with `density` ?
---
### Author:  [@empet](https://discourse.julialang.org/u/empet)
#### Post date: [October 31, 2023, 8:36pm UTC](https://discourse.julialang.org/t/what-does-density-do-when-applied-to-a-distribution-directly/105621/2 "2023-10-31T20:36:00Z")
It’s strange that `density!(Normal(), label="density()")` doesn’t throw an error, because `StatsPlots.density!` is a generic function with 1 method.
```julia
?density # or density!
```
displays that
```julia
density(x)
density!(x)
```
make a line plot of a kernel density estimate of x, where x is an `AbstractVector` of samples for probability density estimation.
Or you passed a distribution, not a sample from that distribution.
---
### Author:  [@mthelm85](https://discourse.julialang.org/u/mthelm85)
#### Post date: [October 31, 2023, 10:00pm UTC](https://discourse.julialang.org/t/what-does-density-do-when-applied-to-a-distribution-directly/105621/3 "2023-10-31T22:00:31Z")
This does seem strange. I’m having a difficult time finding exactly where `density` is defined in the source code…?
---
### Author:  [@johnmyleswhite](https://discourse.julialang.org/u/johnmyleswhite)
#### Post date: [November 1, 2023, 12:40am UTC](https://discourse.julialang.org/t/what-does-density-do-when-applied-to-a-distribution-directly/105621/4 "2023-11-01T00:40:47Z")
This is a use case for `@which`:
```julia
julia> using Distributions, StatsPlots
julia> plot(Normal(), label="plot()")
julia> density!(rand(Normal(), 100_000), label="density(rand())")
julia> density!(Normal(), label="density()")
julia> @which density!(Normal(), label="density()")
kwcall(::NamedTuple, ::typeof(density!), args...)
@ Plots ~/.julia/packages/RecipesBase/BRe07/src/RecipesBase.jl:429
```
That line of code is in this block:
```julia
macro shorthands(funcname::Symbol)
funcname2 = Symbol(funcname, "!")
quote
export $funcname, $funcname2
Core.@ __doc__ $funcname(args...; kw...) =
$RecipesBase.plot(args...; kw..., seriestype = $(Meta.quot(funcname)))
Core.@ __doc__ $funcname2(args...; kw...) =
$RecipesBase.plot!(args...; kw..., seriestype = $(Meta.quot(funcname)))
end |> esc
end
```
---
### Author:  [@nilshg](https://discourse.julialang.org/u/nilshg)
#### Post date: [November 1, 2023, 9:36am UTC](https://discourse.julialang.org/t/what-does-density-do-when-applied-to-a-distribution-directly/105621/5 "2023-11-01T09:36:24Z")
It’s a very old issue:
>
>
> \`\`\`
> using StatsPlots, Distributions
> density(Normal())
> \`\`\`
> currently gives a …weird bimodal distribution
>
> !\[normal\_error\](https://user-images.githubusercontent.com/7264491/60345293-997e5d00-99b0-11e9-8d19-ba28c3e28926.PNG)
>
> This is on Julia v1.1.1
>
> \`\`\`
> Status \`C:\\Users\\~\\.julia\\environments\\v1.1\\Project.toml\`
> \[c52e3926\] Atom v0.8.7
> \[6e4b80f9\] BenchmarkTools v0.4.2
> \[336ed68f\] CSV v0.5.6
> \[a93c6f00\] DataFrames v0.18.3
> \[31c24e10\] Distributions v0.19.2
> \[38e38edf\] GLM v1.2.0
> \[7073ff75\] IJulia v1.18.1
> \[e5e0dc1b\] Juno v0.7.0
> \[ff71e718\] MixedModels v1.1.6
> \[c030b06c\] ODE v2.4.0
> \[91a5bcdd\] Plots v0.25.1
> \[6f49c342\] RCall v0.13.3
> \[d519eb52\] RegressionTables v0.2.0
> \[2913bbd2\] StatsBase v0.30.0
> \[f3b207a7\] StatsPlots v0.11.0
> \`\`\`
---
### Author:  [@dlakelan](https://discourse.julialang.org/u/dlakelan)
#### Post date: [November 1, 2023, 10:32am UTC](https://discourse.julialang.org/t/what-does-density-do-when-applied-to-a-distribution-directly/105621/6 "2023-11-01T10:32:04Z")
It looks like the macro is auto-writing code and this is a special case where it should do something different?
---
### Author:  [@johnmyleswhite](https://discourse.julialang.org/u/johnmyleswhite)
#### Post date: [November 1, 2023, 10:18pm UTC](https://discourse.julialang.org/t/what-does-density-do-when-applied-to-a-distribution-directly/105621/7 "2023-11-01T22:18:12Z")
That is my understanding, although it is bit tricky for me to follow: StatsPlots has a lot of explicit calls to that `@shorthand` macro, but I didn’t see the one for `density`.