gompertz | R Documentation |

`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 )

`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 |

The state process is

*X[t+1]=K^(1-S) X[t]^S eps[t],*

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

*Y[t]~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.

A ‘pomp’ object with simulated data.

More examples provided with pomp:
`SIR models`

,
`blowflies`

,
`childhood disease data`

,
`dacca()`

,
`ebola`

,
`ou2()`

,
`pomp examples`

,
`ricker()`

,
`rw2()`

,
`verhulst()`

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

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