Computes the cosine expansion terms that modify the
shape of distance likelihood functions.
Usage
cosine.expansion(x, expansions)
Value
A 3D array of size nrow(x) X ncol(x) X expansions.
The 'pages' (3rd dimension) of this array are the cosine expansions of
x. i.e., page 1 is the first expansion term of x,
page 2 is the second expansion term of x, etc.
Arguments
x
A numeric matrix of distances at which to evaluate
the expansion series. For distance analysis, x should
be the proportion of the maximum sighting distance
at which a group was sighted, i.e., \(x = d/w\), where \(d\)
is sighting distance and \(w\) is maximum sighting distance.
expansions
A scalar specifying the number of
expansion terms to compute. Must be one of the
integers 1, 2, 3, 4, or 5.
Details
The cosine expansion used here is:
First term: $$h_1(x)=\cos(2\pi x),$$
Second term: $$h_2(x)=\cos(4\pi x),$$
Third term: $$h_3(x)=\cos(6\pi x),$$
Fourth term: $$h_4(x)=\cos(8\pi x),$$
Fifth term: $$h_5(x)=\cos(10\pi x),$$
The maximum number of expansion terms is 5.
The cosine expansion frequency in Rdistance is 2*pi. Each term is two pi more than
the previous. The sine expansion frequency in Rdistance is pi. Consequently,
the sine and cosine expansions fit different models.