spatstat (version 1.55-1)

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)

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.

Value

A single number.

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

See Also

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

Examples

# NOT RUN {
   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)
# }