# simple.expansion: Calculate simple polynomial expansion for detection function... In Rdistance: Distance-Sampling Analyses for Density and Abundance Estimation

 simple.expansion R Documentation

## Calculate simple polynomial expansion for detection function likelihoods

### Description

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

### Usage

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\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, or 4.

### Details

The polynomials computed here are:

• First term:

h_1(x)=x^4,

• Second term:

h_2(x)=x^6,

• Third term:

h_3(x)=x^8,

• Fourth term:

h_4(x)=x^10,

The maximum number of expansion terms computed is 4.

### Value

A matrix of size length(x) X expansions. The columns of this matrix are the Hermite polynomial 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, cosine.expansion, hermite.expansion, and the discussion of user defined likelihoods in dfuncEstim.

### Examples

set.seed(883839)
x <- rnorm(1000) * 100
x <- x[ 0 < x & x < 100 ]
simp.expn <- simple.expansion(x, 4)


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