cosine.expansion {Rdistance} | R Documentation |
cosine.expansion - Cosine expansion terms
Description
Computes the cosine expansion terms used to modify the shape of distance likelihood functions.
Usage
cosine.expansion(x, expansions)
Arguments
x |
A numeric vector of distances at which to evaluate
the expansion series. For distance analysis, |
expansions |
A scalar specifying the number of expansion terms to compute. Must be one of the integers 1, 2, 3, 4, or 5. |
Details
There are, in general, several expansions that can be called cosine. The cosine expansion used here is:
-
First term:
h_1(x)=\cos(2\pi x),
-
Second term:
h_2(x)=\cos(3\pi x),
-
Third term:
h_3(x)=\cos(4\pi x),
-
Fourth term:
h_4(x)=\cos(5\pi x),
-
Fifth term:
h_5(x)=\cos(6\pi x),
The maximum number of expansion terms computed is 5.
Value
A matrix of size length(x)
X expansions
. The columns of this matrix are the cosine expansions of
x
. Column 1 is the first expansion term of x
, column 2 is the second expansion term of x
, and so on
up to expansions
.
See Also
dfuncEstim
, hermite.expansion
, simple.expansion
, and the discussion
of user defined likelihoods in dfuncEstim
.
Examples
x <- seq(0, 1, length = 200)
cos.expn <- cosine.expansion(x, 5)
plot(range(x), range(cos.expn), type="n")
matlines(x, cos.expn, col=rainbow(5), lty = 1)