Rdistance (version 1.3.2)

cosine.expansion: Calcululation 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)

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 scaler specifying the number of expansion terms to compute. Must be one of the integers 1, 2, 3, 4, or 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.

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

F.dfunc.estim, hermite.expansion, simple.expansion, and the discussion of user defined likelihoods in F.dfunc.estim.

Examples

# NOT RUN {
set.seed(33328)
x <- rnorm(1000) * 100
x <- x[ 0 < x & x < 100 ]
cos.expn <- cosine.expansion( x, 5 )
# }