dtm function

Density for Time Spent in Moving or Resting

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

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.

Returns

a vector of the density evaluated at w.

Details

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

Functions

• dtr(): Density of time spent in resting

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)

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.