Computes Hermite expansion terms for use in
distance analysis. The Hermite (and other expansions) allow "wiggle" in
estimated distance functions.
Usage
hermite.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
There are, in general, several expansions that can be called Hermite. Let \(w = 4x - 2\).
Rdistance's Hermite expansions are:
First term: $$h_1(w) = w + 2,$$
Second term: $$h_2(w) = w^2 - 4,$$
Third term: $$h_3(w) = w^3 - 3w + 2,$$
Fourth term: $$h_4(w) = w^4 - 6w^2 + 8,$$
The maximum number of expansion terms computed is 4.