spatstat.explore (version 3.1-0)

kernel.squint: 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)

Value

A single number.

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.

Author

Adrian Baddeley , Rolf Turner and Ege Rubak and Martin Hazelton

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, $$ R = \int_{-\infty}^{\infty} k(x)^2 \, {\rm d}x $$ where \(k(x)\) is the kernel with bandwidth bw.

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)