Epanechnikov Kernel
Mathematical and statistical functions for the Epanechnikov kernel defined by the pdf,
f(x) = 3/4(1-x^2)
over the support x ε (-1,1).
The quantile function is omitted as no closed form analytic expressions could be found, decorate with FunctionImputation for numeric results.
distr6::Distribution -> distr6::Kernel -> Epanechnikov
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
pdfSquared2Norm()
The squared 2-norm of the pdf is defined by
\int_a^b (f_X(u))^2 du
where X is the Distribution, f_X is its pdf and a, b are the distribution support limits.
Epanechnikov$pdfSquared2Norm(x = 0, upper = Inf)
x(numeric(1))
Amount to shift the result.
upper(numeric(1))
Upper limit of the integral.
cdfSquared2Norm()
The squared 2-norm of the cdf is defined by
\int_a^b (F_X(u))^2 du
where X is the Distribution, F_X is its pdf and a, b are the distribution support limits.
Epanechnikov$cdfSquared2Norm(x = 0, upper = 0)
x(numeric(1))
Amount to shift the result.
upper(numeric(1))
Upper limit of the integral.
variance()
The variance of a distribution is defined by the formula
var_X = E[X^2] - E[X]^2
where E_X is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.
Epanechnikov$variance(...)
...Unused.
clone()
The objects of this class are cloneable with this method.
Epanechnikov$clone(deep = FALSE)
deepWhether to make a deep clone.
Other kernels:
Cosine,
LogisticKernel,
NormalKernel,
Quartic,
Sigmoid,
Silverman,
TriangularKernel,
Tricube,
Triweight,
UniformKernel
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