Silverman | R Documentation |
Mathematical and statistical functions for the Silverman kernel defined by the pdf,
f(x) = exp(-|x|/√{2})/2 * sin(|x|/√{2} + π/4)
over the support x ε R.
The cdf and quantile functions are omitted as no closed form analytic expressions could be found, decorate with FunctionImputation for numeric results.
distr6::Distribution
-> distr6::Kernel
-> Silverman
name
Full name of distribution.
short_name
Short name of distribution for printing.
description
Brief description of the distribution.
new()
Creates a new instance of this R6 class.
Silverman$new(decorators = NULL)
decorators
(character())
Decorators to add to the distribution during construction.
pdfSquared2Norm()
The squared 2-norm of the pdf is defined by
\int_a^b (f_X(u))^2 du
where X is the Distribution, f_X is its pdf and a, b are the distribution support limits.
Silverman$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.
Silverman$cdfSquared2Norm(x = 0, upper = 0)
x
(numeric(1))
Amount to shift the result.
upper
(numeric(1))
Upper limit of the integral.
variance()
The variance of a distribution is defined by the formula
var_X = E[X^2] - E[X]^2
where E_X is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.
Silverman$variance(...)
...
Unused.
clone()
The objects of this class are cloneable with this method.
Silverman$clone(deep = FALSE)
deep
Whether to make a deep clone.
Other kernels:
Cosine
,
Epanechnikov
,
LogisticKernel
,
NormalKernel
,
Quartic
,
Sigmoid
,
TriangularKernel
,
Tricube
,
Triweight
,
UniformKernel
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