R: Moment of Smoothing Kernel

kernel.moment {spatstat.core} | R Documentation

## Moment of Smoothing Kernel

### Description

Computes the complete or incomplete mth 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).

### 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

integral[-Inf][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`.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au and Martin Hazelton.

### See Also

`density.default`, `dkernel`, `kernel.factor`,

### Examples

       kernel.moment(1, 0.1, "epa")
       curve(kernel.moment(2, x, "epa"), from=-1, to=1)

[Package spatstat.core version 2.3-1 Index]