integrateOneStepPoints: Integrate Point-survey One-step function

Description

Compute integral of the one-step distance function for point-surveys.

Usage

integrateOneStepPoints(
  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 $$\int_0^{w} x(\frac{p}{\theta_i}I(0\leq x \leq \theta_i) + \frac{1-p}{w - \theta_i}I(\theta_i < x \leq w)) dx = \frac{\theta_i}{2p}((1-p)w + \theta_i),$$ where $w = w.hi - w.lo$, $\theta_i$ is the estimated one-step distance function threshold for the i-th observed distance, and $p$ is the estimated one-step proportion.

Examples

Run this code


fit <- dfuncEstim(thrasherDf, dist~1, likelihood = "oneStep")
integrateOneStepPoints(fit, newdata = data.frame(`(Intercept)`=1))
EDR(fit, newdata = data.frame(`(Intercept)`=1))

# Check: 
Theta <- exp(fit$par[1])
Theta <- setUnits(Theta, "m")
p <- fit$par[2]
w.hi <- fit$w.hi
w.lo <- fit$w.lo
g.at0 <- w.lo
g.atT <- Theta
g.atTPlusFuzz <- (((1-p) * Theta) / ((w.hi - Theta) * p))*Theta
g.atWhi <- (((1-p) * Theta) / ((w.hi - Theta) * p))*w.hi
area.0.to.T <- (Theta - w.lo) * (g.atT - g.at0) / 2 # triangle; Theta^2/2
area.T.to.w <- (w.hi - Theta) * (g.atTPlusFuzz + g.atWhi) / 2 # trapazoid
area <- area.0.to.T + area.T.to.w
edr <- sqrt( 2*area )