Epanechnikov kernel density

I am trying to use a Epanechnikov kernel density estimator in KernelDensity.jl. Surprisingly, this is not implemented, but it should be possible to accomplish by extending the function kernel_dist. I have been unable to match the results from R. It is not clear to me whether this is because I extended kernel_dist incorrectly or because the interpolation functions differ. So I was hoping that someone who has more familiarity with the topic might provide some help.

Julia code:

using KernelDensity,Distributions
import KernelDensity: kernel_dist
kernel_dist(::Type{Epanechnikov},w::Real) = Epanechnikov(0.0,w)
data =  [0.952,0.854,0.414,0.328,0.564,0.196,0.096,0.366,0.902,0.804]
kd = kde(data;kernel=Epanechnikov)
dist = InterpKDE(kd)

Result = 1.3029

R code:

data =  c(0.952,0.854,0.414,0.328,0.564,0.196,0.096,0.366,0.902,0.804)
kd = density(data,kernel = "epanechnikov")
f = approxfun(kd)

Result = .9670

I repeated the comparison for a standard normal with 10^5 samples and found a discrepancy, albeit a smaller one: .3818 for R which is very close to the theoretical true value and .3782 for Julia.

For small sample, implementation differences may create significant deviations. For example by fixing the bandwidth, grid points and interpolation, you can get pretty similar results:

using KernelDensity,Distributions,Interpolations
import KernelDensity: kernel_dist
kernel_dist(::Type{Epanechnikov},w::Real) = Epanechnikov(0.0,w)
data =  [0.952,0.854,0.414,0.328,0.564,0.196,0.096,0.366,0.902,0.804]
kd   = kde(data, range(-5.0, 5.0,length=2048); kernel=Epanechnikov, bandwidth=1.0*sqrt(5))
dist = InterpKDE(kd, BSpline(Linear()))

julia> pdf(dist,.3)

In R:

> data =  c(0.952,0.854,0.414,0.328,0.564,0.196,0.096,0.366,0.902,0.804)
> kd   = density(data,bw = 1.0, kernel = "epanechnikov",from=-5.0,to=5.0, n=2048)
> f    = approxfun(kd)
> f(.3)
[1] 0.3254264361

Thanks. I had a suspicion that there were implementation differences lurking somewhere.