# 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. 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.

##### See Also

density.default, dkernel, kernel.factor,

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

Documentation reproduced from package spatstat, version 1.56-1, License: GPL (>= 2)

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