gompertz {pomp} | R Documentation |
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 |
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))