pomp (version 0.39-3)

gompertz: Gompertz model with log-normal observations.

Description

gompertz is a pomp object encoding a stochastic Gompertz population model with log-normal measurement error.

Usage

data(gompertz)

Details

The state process is $X_{t+1} = K^{(1-S)} X_{t}^S \varepsilon_{t}$, where $S=e^{-r}$ and the $\varepsilon_t$ are i.i.d. lognormal random deviates with variance $\sigma^2$. The observed variables $Y_t$ are distributed as $\mathrm{lognormal}(\log{X_t},\tau)$. 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 model is parameterized internally by the logarithms of $r$, $K$, $\sigma$, and $\tau$; the initial condition is parameterized directly. The pomp object includes parameter transformations to and from this internal parameterization.

See Also

pomp-class and the introductory vignette vignette("intro_to_pomp").

Examples

data(gompertz)
plot(gompertz)
coef(gompertz)
coef(gompertz,transform=TRUE)