kernel.moment: Moment of Smoothing Kernel

In spatstat/spatstat.core: Core Functionality of the 'spatstat' Family

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

\int_{-\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).

Value

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

Author(s)

\adrian

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)

spatstat/spatstat.core documentation built on July 26, 2024, 10:44 a.m.