simple.expansion function

Calculate simple polynomial expansion for detection function likelihoods

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

simple.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 ($d <= w$), 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, or 4.

Returns

A matrix of size length(x) X expansions. The columns of this matrix are the Simple polynomial expansions of x. Column 1 is the first expansion term of x, column 2 is the second x, and so on up to expansions.

Details

The polynomials computed here are:

• First term :

• Second term :

• Third term :

• Fourth term :

The maximum number of expansion terms computed is 4.

Examples

x <- seq(0, 1, length = 200)
simp.expn <- simple.expansion(x, 4)
plot(range(x), range(simp.expn), type="n")
matlines(x, simp.expn, col=rainbow(4), lty = 1)

See Also

dfuncEstim, cosine.expansion, hermite.expansion