spatstat.core (version 1.65-5)

kernel.moment: Moment of Smoothing Kernel

Description

Computes the complete or incomplete $m$th 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).

Value

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

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 $${\int }_{-\mathrm{\infty }}^r{t}^{m}k(t)dt$$ 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).

See Also

density.default, dkernel, kernel.factor,

Examples

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