`sim.seasonalNoise.Rd`

Generation of a cyclic model of a Poisson distribution as background data for a simulated timevector.

The mean of the Poisson distribution is modelled as: $$\mu = \exp(A \sin( frequency \cdot \omega \cdot (t + \phi)) + \alpha + \beta * t + K * state)$$

```
sim.seasonalNoise(A = 1, alpha = 1, beta = 0, phi = 0,
length, frequency = 1, state = NULL, K = 0)
```

- A
amplitude (range of sinus), default = 1.

- alpha
parameter to move along the y-axis (negative values not allowed) with alpha > = A, default = 1.

- beta
regression coefficient, default = 0.

- phi
factor to create seasonal moves (moves the curve along the x-axis), default = 0.

- length
number of weeks to model.

- frequency
factor to determine the oscillation-frequency, default = 1.

- state
if a state chain is entered the outbreaks will be additional weighted by K.

- K
additional weigth for an outbreak which influences the distribution parameter mu, default = 0.

an object of class `seasonNoise`

which includes the modelled
timevector, the parameter `mu`

and all input parameters.

M. Höhle, A. Riebler, C. Lang

```
season <- sim.seasonalNoise(length = 300)
plot(season$seasonalBackground,type = "l")
# use a negative timetrend beta
season <- sim.seasonalNoise(beta = -0.003, length = 300)
plot(season$seasonalBackground,type = "l")
```