Computes the cosine expansion terms used to modify the
shape of distance likelihood functions.
Usage
cosine.expansion(x, expansions)
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.
Arguments
x
A numeric vector of distances at which to evaluate
the expansion series. For distance analysis, x is
of the proportion of a strip transect's half-width
at which a group of individuals were sighted, i.e., \(d/w\).
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.
See Also
dfuncEstim, hermite.expansion, simple.expansion, and the discussion
of user defined likelihoods in dfuncEstim.