# cosine.expansion: calculation of cosine expansion for detection function... In Rdistance: Distance-Sampling Analyses for Density and Abundance Estimation

 cosine.expansion R Documentation

## calculation 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 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.

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

### Examples

set.seed(33328)
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.