R: Integral of Squared Kernel

kernel.squint {spatstat} | R Documentation

## Integral of Squared Kernel

### Description

Computes the integral of the squared kernel, for the kernels used in density estimation for numerical data.

### Usage

      kernel.squint(kernel = "gaussian", bw=1)

### Arguments

`kernel` | String name of the kernel. Options are `"gaussian"`, `"rectangular"`, `"triangular"`, `"epanechnikov"`, `"biweight"`, `"cosine"` and `"optcosine"`. (Partial matching is used).
`bw` | Bandwidth (standard deviation) of the kernel.

### Details

Kernel estimation of a probability density in one dimension is performed by `density.default` using a kernel function selected from the list above.

This function computes the integral of the squared kernel,

R = integral of k(x)^2 dx from x = -infinity to x = +infinity

where k(x) is the kernel with bandwidth `bw`.

### Value

A single number.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk and Martin Hazelton

### See Also

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

### Examples

       kernel.squint("gaussian", 3)

       # integral of squared Epanechnikov kernel with half-width h=1
       h <- 1
       bw <- h/kernel.factor("epa")
       kernel.squint("epa", bw)

[Package spatstat version 1.54-0 Index]