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

View source: R/cosine.expansion.R

cosine.expansionR Documentation

calculation of cosine expansion for detection function likelihoods


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


cosine.expansion(x, expansions)



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


A scalar specifying the number of expansion terms to compute. Must be one of the integers 1, 2, 3, 4, or 5.


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.


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.


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

Rdistance documentation built on July 9, 2023, 6:46 p.m.