KernelDensity.jl
Kernel density estimators for julia.
Usage
Univariate
The main accessor function is kde
:
kde(data)
will construct a UnivariateKDE
object from the real vector data
. The
optional keyword arguments are

boundary
: the lower and upper limits of the kde as a tuple. Due to the fourier transforms used internally, there should be sufficient spacing to prevent wraparound at the boundaries. 
npoints
: the number of interpolation points to use. The function uses fast Fourier transforms (FFTs) internally, so for optimal efficiency this should be a power of 2 (default = 2048). 
kernel
: the distributional family from Distributions.jl to use as the kernel (default =Normal
). To add your own kernel, extend the internalkernel_dist
function. 
bandwidth
: the bandwidth of the kernel. Default is to use Silverman's rule.
A related function
kde_lscv(data)
will construct a UnivariateKDE
object, with the bandwidth selected by
leastsquares cross validation. It accepts the above keyword arguments, except
bandwidth
.
There are also some slightly more advanced interfaces:
kde(data, midpoints::Range)
allows specifying the internal grid to use. Optional keyword arguments are
kernel
and bandwidth
.
kde(data, dist::Distribution)
allows specifying the exact distribution to use as the kernel. Optional
keyword arguments are boundary
and npoints
.
kde(data, midpoints::Range, dist::Distribution)
allows specifying both the distribution and grid.
Bivariate
The usage mirrors that of the univariate case, except that data
is now
either a tuple of vectors
kde((xdata, ydata))
or a matrix with two columns
kde(datamatrix)
Similarly, the optional arguments all now take tuple arguments:
e.g. boundary
now takes a tuple of tuples ((xlo,xhi),(ylo,yhi))
.
Interpolation
The KDE objects are stored as gridded density values, with attached
coordinates. These are typically sufficient for plotting (see below), but
intermediate values can be interpolated using the
Grid.jl package via the pdf
method
(extended from Distributions.jl).
pdf(k::UnivariateKDE, x)
pdf(k::BivariateKDE, x, y)
where x
and y
are real numbers or arrays.
If you are making multiple calls to pdf
, it will be more efficient to
construct an intermediate InterpKDE
to store the intermediate InterpGrid
object:
ik = InterpKDE(k)
pdf(ik, x)
InterpKDE
can also take additional arguments specifying the
BoundaryCondition
(default=BCnan
) and InterpType
(default=
InterpQuadratic
).
Plotting
The Winston.jl and PyPlot.jl plotting packages are currently supported. See the ijulia notebooks:
We plan to include support for other plotting packages: please file an issue if your favourite one is not yet available.