integrateNegexpLines: Integrate Negative exponential

Description

Compute integral of the negative exponential distance function.

Usage

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

Value

A vector of areas under the distance functions represented in object. 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(exp(fit$par),1)). If a matrix, each row corresponds to a distance function and each column is a parameter. The first column is the parameter related to sighting covariates and must be transformed to the "real" space (i.e., inverse link, which is $exp()$, must be applied outside this routine). If object is a matrix, it should not have measurement units because only derived quantities (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 $$\int_0^{w} e^{-a_i x} dx = \frac{1}{a_i} (1 - e^{-a_i w}),$$ where $w = w.hi - w.lo$ and $a_i$ is the estimated negative exponential 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(-5, -0.5)
w.hi <- 125
w.lo <- 20
ml <- list(
    mf = model.frame(d ~ obs)
  , par = beta 
  , likelihood = "negexp"
  , w.lo = w.lo %#% "m"
  , w.hi = w.hi %#% "m"
  , expansions = 0
)
class(ml) <- "dfunc"
integrateNegexpLines(ml)

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