smam (version 0.7.2)

rMRB: Sampling from a Moving-Resting bridge

Description

A moving-resting process consists of two states: moving and resting. The transition between the two states is modeled by an alternating renewal process, with exponentially distributed duration. An animal stays at the same location while resting, and moves according to a Brownian motion while moving. A moving-resting bridge is an extension of Brownian bridge that uses moving-resting process to bridge given starting point and ending point.

Usage

rMRB(time, start_pt, end_pt, lamM, lamR, sigma, s0)

Value

A data.frame whose first column is the time points and whose other columns are coordinates of the locations.

Arguments

time

time points at which observations are to be simulated

start_pt

the start point location of Brownian bridge (numeric for one dimension, vector for multiple dimension)

end_pt

the end point location of Brownian brige (numeric for one dimension, vector for multiple dimension)

lamM

rate parameter of the exponential duration while moving

lamR

rate parameter of the exponential duration while resting

sigma

volatility parameter of the Brownian motion while moving

s0

the state at time 0, must be one of "m" or "r", for moving and resting, respectively

Examples

tgrid <- seq(0, 10, length=1001)
## make it irregularly spaced
tgrid <- sort(sample(tgrid, 800))

## a 2-dim moving-resting bridge starting from c(0, 0)
## and ending at c(10, -10)
dat <- rMRB(tgrid, start_pt = c(0, 0), end_pt = c(10, -10),
            lamM = 1, lamR = 1, sigma = 1, "m")
par(mfrow = c(2, 1))
plot(dat[,1], dat[,2], xlab="t", ylab="X(t)", type='l')
plot(dat[,1], dat[,3], xlab="t", ylab="X(t)", type='l')
par(mfrow = c(1, 1))