Computes the complete or incomplete \(m\)th moment of a smoothing kernel.

`kernel.moment(m, r, kernel = "gaussian")`

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).

A single number, or a numeric vector of the same length as `r`

.

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.
Here \(k(t)\) is the **standard form** of the kernel,
which has support \([-1,1]\) and
standard deviation \(sigma = 1/c\) where `c = kernel.factor(kernel)`

.

# NOT RUN { kernel.moment(1, 0.1, "epa") curve(kernel.moment(2, x, "epa"), from=-1, to=1) # }