integrateHalfnormPoints: Integrate Half-normal Point transects

Description

Compute integral of the half-normal distance function for point surveys.

Usage

integrateHalfnormPoints(
  object,
  newdata = NULL,
  w.lo = NULL,
  w.hi = NULL,
  Units = NULL
)

Value

A vector of areas under distance functions. If object is a distance function and newdata is specified, the returned vector's length is nrow(newdata). If object is a distance function and newdata is NULL, returned vector's length is length(distances(object)). If object is a matrix, return's length is nrow(object).

Arguments

object: Either an Rdistance fitted distance function (an object that inherits from class "dfunc"; usually produced by a call to dfuncEstim), or a matrix of canonical distance function parameters (e.g., matrix(fit$par,1)). If a matrix, each row corresponds to a distance function and each column is a parameter. If object is a matrix, it should not have measurement units. Only quantities derived from function parameters (e.g., ESW) have units. Rdistance function parameters themselves never have units.
newdata: A data frame containing new values for the distance function covariates. If NULL and object is a fitted distance function, the observed covariates stored in object are used (behavior similar to predict.lm). Argument newdata is ignored if object is a matrix.
w.lo: Minimum sighting distance or left-truncation value if object is a matrix. Ignored if object is a fitted distance function. Must have physical measurement units.
w.hi: Maximum sighting distance or right-truncation value if object is a matrix. Ignored if object is a fitted distance function. Must have physical measurement units.
Units: Physical units of sighting distances if object is a matrix. Sighting distance units can differ from units of w.lo or w.hi. Ignored if object is a fitted distance function.

Details

Returned integrals are $$\int_0^{w} xe^{-x^2/2\sigma_i^2} dx = 0.5\sigma_i^2(1 - e^{-w^2/2\sigma_i^2}),$$ where $w = w.hi - w.lo$ and $\sigma_i$ is the estimated half-normal distance function parameter for the i-th observed distance.

Examples

Run this code


# Fake distance function object w/ minimum inputs for integration
d <- rep(1,4) %m%. # Only units needed, not values
obs <- factor(rep(c("obs1", "obs2"), 2))
beta <- c(3.5, -0.5)
w.hi <- 125
w.lo <- 20
ml <- list(
    mf = model.frame(d ~ obs)
  , par = beta 
  , likelihood = "halfnorm"
  , w.lo = w.lo %#% "m"
  , w.hi = w.hi %#% "m"
)
class(ml) <- "dfunc"
integrateHalfnormPoints(ml)

# Check: Integral of x exp(-x^2/(2*s^2)) from 0 to w = w.hi-w.lo
sigma <- exp(c(beta[1], beta[1] + beta[2]))
w <- w.hi - w.lo
intgral <- sigma^2 * (1 - exp(-w^2 / (2*sigma^2)))
intgral

# Effective detection radius
sqrt(2 * intgral)