dtm: Density for Time Spent in Moving or Resting

In smam: Statistical Modeling of Animal Movements

Density for Time Spent in Moving or Resting

Description

Density for time spent in moving or resting in a time interval, unconditional or conditional on the initial state.

Usage

dtm(w, t, lamM, lamR, s0 = NULL)

dtr(w, t, lamM, lamR, s0 = NULL)

Arguments

w	time points at which the density is to be evaluated
t	length of the time interval
lamM	rate parameter of the exponentially distributed duration in moving
lamR	rate parameter of the exponentially distributed duration in resting
s0	initial state. If NULL, the unconditional density is returned; otherwise, it is one of "m" or "s", standing for moving and resting, respectively, and the conditional density is returned given the initial state.

Details

dtm returns the density for time in moving; dtr returns the density for time in resting.

Value

a vector of the density evaluated at w.

Functions

• dtr(): Density of time spent in resting

References

Yan, J., Chen, Y., Lawrence-Apfel, K., Ortega, I. M., Pozdnyakov, V., Williams, S., and Meyer, T. (2014) A moving-resting process with an embedded Brownian motion for animal movements. Population Ecology. 56(2): 401–415.

Examples

lamM <- 1
lamR <- c(1/2, 1, 2)
lr <- length(lamR)
totalT <- 10
old.par <- par(no.readonly=TRUE)
par(mfrow=c(1, 2), mar=c(2.5, 2.5, 1.1, 0.1), mgp=c(1.5, 0.5, 0), las=1)
curve(dtm(x, totalT, 1, 1/2, "m"), 0, totalT, lty=1, ylim=c(0, 0.34),
      xlab="M(10)", ylab="density")
curve(dtm(x, totalT, 1, 1, "m"), 0, totalT, lty=2, add=TRUE)
curve(dtm(x, totalT, 1, 2, "m"), 0, totalT, lty=3, add=TRUE)
mtext(expression("S(0) = 1"))
legend("topleft", legend = expression(lambda[r] == 1/2, lambda[r] == 1,
       lambda[r] == 2), lty = 1:lr)
curve(dtm(x, totalT, 1, 1/2, "r"), 0, totalT, lty=1, ylim=c(0, 0.34),
      xlab="M(10)", ylab="density")
curve(dtm(x, totalT, 1, 1, "r"), 0, totalT, lty=2, add=TRUE)
curve(dtm(x, totalT, 1, 2, "r"), 0, totalT, lty=3, add=TRUE)
mtext(expression("S(0) = 0"))
legend("topleft", legend = expression(lambda[r] == 1/2, lambda[r] == 1,
      lambda[r] == 2), lty = 1:lr)
par(old.par)

smam documentation built on Aug. 21, 2023, 9:09 a.m.