gompertz() constructs a ‘pomp’ object encoding a stochastic Gompertz population model with log-normal measurement error.
gompertz(
K = 1,
r = 0.1,
sigma = 0.1,
tau = 0.1,
X_0 = 1,
times = 1:100,
t0 = 0
)A ‘pomp’ object with simulated data.
carrying capacity
growth rate
process noise intensity
measurement error s.d.
value of the latent state variable X at the zero time
observation times
zero time
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.
More examples provided with pomp:
blowflies,
childhood_disease_data,
compartmental_models,
dacca(),
ebola,
ou2(),
pomp_examples,
ricker(),
rw2(),
verhulst()
plot(gompertz())
plot(gompertz(K=2,r=0.01))
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