Rdistance (version 3.0.0)

cosine.expansion: calculation of cosine expansion for detection function likelihoods

Description

Computes the cosine expansion terms used in the likelihood of a distance analysis. More generally, will compute a cosine expansion of any numeric vector.

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

In a distance analysis, x is a numeric vector of the proportion of a strip transect's half-width at which a group of individuals were sighted. If \(w\) is the strip transect half-width or maximum sighting distance, and \(d\) is the perpendicular off-transect distance to a sighted group (\(d\leq w\)), x is usually \(d/w\). More generally, x is a vector of numeric values

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.

Examples

set.seed(33328)
  x <- rnorm(1000) * 100
  x <- x[ 0 < x & x < 100 ]
  cos.expn <- cosine.expansion(x, 5)