# kernel.moment

##### Moment of Smoothing Kernel

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

- Keywords
- methods, smooth, nonparametric

##### 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).

##### 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.
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)`

.

##### Value

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

.

##### See Also

##### Examples

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

*Documentation reproduced from package spatstat, version 1.57-1, License: GPL (>= 2)*