spatstat (version 1.64-1)

# 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 $$\int_{-\infty}^r t^m k(t) dt$$ 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).

density.default, dkernel, kernel.factor,
# NOT RUN {