sine.expansion: Sine expansion terms

In Rdistance: Density and Abundance from Distance-Sampling Surveys

Sine expansion terms

Description

Computes the sine expansion terms that modify the shape of distance likelihood functions.

Usage

sine.expansion(x, expansions)

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 sine expansion used here is:

• First term:

  h_1(x)=\sin(2\pi x)/2,

• Second term:

  h_2(x)=\sin(3\pi x)/2,

• Third term:

  h_3(x)=\sin(4\pi x)/2,

• Fourth term:

  h_4(x)=\sin(5\pi x)/2,

• Fifth term:

  h_5(x)=\sin(6\pi x)/2,

The maximum number of expansion terms is 5.

The sine expansion frequency in Rdistance is pi. Each term is one pi more than the previous. The cosine expansion frequency in Rdistance is 2*pi. Consequently, the sine and cosine expansions fit different models.

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.

See Also

dfuncEstim, cosine.expansion

Examples

x <- matrix(seq(0, 1, length = 200), ncol = 1)
sin.expn <- sine.expansion(x, 5)
plot(range(x), range(sin.expn), type="n")
matlines(x, sin.expn[,1,1:5], col=rainbow(5), lty = 1)

Rdistance documentation built on Jan. 10, 2026, 1:07 a.m.