smam (version 0.2-2)

dtm: 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

the length of the time interval

lamM

the rate parameter of the exponentially distributed moving stage duration

lamR

the rate parameter of the exponentially distributed resting stage duration

s0

the 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.

Value

a vector of the density evaluated at w

References

Yan, J., Chen, Y., Lawrence-Apfel, K., Ortega, I. M., Pozdnyakoc, V., Williams, S., and Meyer, T. (2013+) A moving-resting process with an embedded Brownian motion for animal movements. Population Ecology. Forthcoming.

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)