gompertz: Gompertz model with log-normal observations.

In kidusasfaw/pomp: Statistical Inference for Partially Observed Markov Processes

Description

gompertz() constructs a ‘pomp’ object encoding a stochastic Gompertz population model with log-normal measurement error.

Usage

gompertz(K = 1, r = 0.1, sigma = 0.1, tau = 0.1, X_0 = 1,
  times = 1:100, t0 = 0)

Arguments

K	carrying capacity
r	growth rate
sigma	process noise intensity
tau	measurement error s.d.
X_0	value of the latent state variable X at the zero time
times	observation times
t0	zero time

Details

The state process is X[t+1]=K^(1-S) X[t]^S eps[t], where S=e^{-r} and the eps[t] are i.i.d. lognormal random deviates with variance sigma^2. The observed variables Y_t are distributed as lognormal(log(X[t]),tau). Parameters include the per-capita growth rate r, the carrying capacity K, the process noise s.d. sigma, the measurement error s.d. tau, and the initial condition X[0]. The ‘pomp’ object includes parameter transformations that log-transform the parameters for estimation purposes.

Value

A ‘pomp’ object with simulated data.

See Also

Other pomp examples: blowflies, dacca, measles, ou2, ricker, rw2, sir_models, verhulst

Examples

plot(gompertz())
plot(gompertz(K=2,r=0.01))

kidusasfaw/pomp documentation built on May 20, 2019, 2:59 p.m.