gompertz function

Gompertz model with log-normal observations.

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

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

Returns

A pomp object with simulated data.

Details

The state process is

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

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.

Examples

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

See Also

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