kernel.moment: Incomplete Moment of Smoothing Kernel

In spatstat.explore: Exploratory Data Analysis for the 'spatstat' Family

Incomplete Moment of Smoothing Kernel

Description

Computes the complete or incomplete mth moment of a smoothing kernel.

Usage

  kernel.moment(m, r, kernel = "gaussian", mean=0, sd=1/kernel.factor(kernel))

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).
mean,sd	Optional numerical values giving the mean and 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. For more information about these kernels, see density.default.

The function kernel.moment computes the 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.

Note that, if mean and sd are not specified, the calculations assume that 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).

The code uses the explicit analytic expressions when m = 0, 1, 2 and numerical integration otherwise.

Value

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

Author(s)

\adrian

and \martinH.

See Also

density.default, dkernel, kernel.factor, kernel.squint

Examples

   kernel.moment(1, 0.1, "epa")
   curve(kernel.moment(2, x, "epa"), from=-1, to=1)

spatstat.explore documentation built on Oct. 23, 2023, 1:07 a.m.