gompertz {pomp}

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

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.

Value

A ‘pomp’ object with simulated data.

See Also

More examples provided with pomp: blowflies, childhood_disease_data, compartmental_models, dacca(), ebola, ou2(), pomp_examples, ricker(), rw2(), verhulst()

Examples

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