| kernel.moment {spatstat.univar} | R Documentation |
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 |
kernel |
String name of the kernel.
Options are
|
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 Baddeley Adrian.Baddeley@curtin.edu.au and Martin Hazelton Martin.Hazelton@otago.ac.nz.
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)