Computes the complete or incomplete $m$th moment of a
smoothing kernel.
Usage
kernel.moment(m, r, kernel = "gaussian")
Arguments
m
Exponent (order of moment).
An integer.
r
Upper limit of integration for the incomplete moment.
A numeric value or numeric vector.
Set r=Inf to obtain the complete moment.
kernel
String name of the kernel.
Options are
"gaussian", "rectangular",
"triangular",
"epanechnikov",
"biweight",
"cosine" and "optcosine".
(Partial matching is used).
Value
A single number, or a numeric vector of the same length as r.
Details
Kernel estimation of a probability density in one dimension
is performed by density.default
using a kernel function selected from the list above.
For more information about these kernels,
see density.default.
The function kernel.moment computes the partial integral
$$
\int_{-\infty}^r t^m k(t) dt
$$
where $k(t)$ is the selected kernel, $r$ is the upper limit of
integration, and $m$ is the exponent or order.