cosine.expansion function

cosine.expansion - Cosine expansion terms

Computes the cosine expansion terms used to modify the shape of distance likelihood functions.

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.

Returns

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 :

• Second term :

• Third term :

• Fourth term :

• Fifth term :

The maximum number of expansion terms computed is 5.

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)

See Also

dfuncEstim, hermite.expansion, simple.expansion, and the discussion of user defined likelihoods in dfuncEstim.