kernel.moment

0th

Percentile

Moment of Smoothing Kernel

Computes the complete or incomplete $m$th moment of a smoothing kernel.

Keywords
methods, smooth, nonparametric
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.

Value

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

See Also

density.default, dkernel, kernel.factor,

Aliases
  • kernel.moment
Examples
   kernel.moment(1, 0.1, "epa")
   curve(kernel.moment(2, x, "epa"), from=-1, to=1)
Documentation reproduced from package spatstat, version 1.48-0, License: GPL (>= 2)

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