pomp (version 4.2)

gompertz: Gompertz model with log-normal observations.

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

Value

A ‘pomp’ object with simulated data.

Details

The state process is $$X_{t+1} = K^{1-S} X_{t}^S \epsilon_{t},$$ where \(S=e^{-r}\) and the \(\epsilon_t\) are i.i.d. lognormal random deviates with variance \(\sigma^2\). The observed variables \(Y_t\) are distributed as $$Y_t\sim\mathrm{lognormal}(\log{X_t},\tau).$$ 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.

See Also

More examples provided with pomp: SIR models, blowflies, childhood disease data, dacca(), ebola, ou2(), pomp examples, ricker(), rw2(), verhulst()

Examples

# NOT RUN {
plot(gompertz())
plot(gompertz(K=2,r=0.01))

# }