cosine.expansion: cosine.expansion - Cosine expansion terms

In Rdistance: Density and Abundance from Distance-Sampling Surveys

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, 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.

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)

Rdistance documentation built on April 12, 2025, 1:12 a.m.