Kernel Density Estimate boundary problems

Specific Domains Statistics
1

Hello everyone,

I am currently trying to calculate probability density curves using the KernelDensity.jl package, however I ran into some issues due to the nature of my data.

I am not a statistician so i will have to explain my problem in layman terms…

The data vector x, I want to calculate the kde of, consist of positive integers including zero, (x_i ∈ Z ≥ 0) which has to be reflected in the density plot.

I know that KernelDensity.kde uses the Normal distribution by default, thus there is no positive support.

x = 0:1:1e4
KDE = kde(x,kernel=Normal)
plot(KDE.x,KDE.density)

In this uniform x case I can simply add this border argument to the kde call to get rid of any x < 0.

KDE = kde(x, boundary=(0,1e4), kernel = Normal)

However my real distribution of x is tailed,

x = round.(rand(LogNormal(3,1),1000))
KDE = kde(x, boundary = extrema(x), kernel = Normal)

and then the boundary argument just wraps the plot over zero.

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I tried to adapt the underlying kernel_dist method with a truncated version of the Normal distribution, but that threw an error.

kernel_dist(::Type{Truncated},w::Real) = truncated(Normal(0.0,w);lower = 0)
KDE = kde(x, kernel = Truncated)

>ERROR: MethodError: no method matching Truncated(::Float64, ::Float64)

So my questions are 1: what am I doing wrong in adding my own kernel distribution; and 2: is this even the correct approach to the probability density?

I hope this question is somewhat clear and Thank you all in advance!

2

Since your values are discrete, it doesnt make much sense to compute densities, right? Why not histograms?

Also, take a look into AverageShiftedHistograms.jl as an alternative to KDEs.

1 Like
3

Yes, you are right, in the discrete case a histogram makes more sense, however, the values of x are discrete since they are obtained through a gillespie simulation, i want to get the density to be able to compare those distributions with the ones from the continuous analytical solution. I already took a look at AverageShiftedHistograms and it seems like a great alternative- however I ran into the same issue of negative events (x).

4

If you want to compare continuous distributions, then check DensityRatioEstimation.jl it only requires samples.