Depending on the current transformation \(h(y)= \{y, \sqrt{y}, y^{2/3}\}\),

$$V(h(y_0)-h(\mu_0))=V(h(y_0))+V(h(\mu_0))$$

is used to compute a prediction interval. The prediction variance
consists of a component due to the variance of having a single
observation and a prediction variance.

## Usage

`algo.farrington.threshold(pred,phi,alpha=0.01,skewness.transform="none",y)`

## Arguments

- pred
A GLM prediction object

- phi
Current overdispersion parameter (superflous?)

- alpha
Quantile level in Gaussian based CI, i.e. an \((1-\alpha)\cdot 100\%\)
confidence interval is computed.

- skewness.transform
Skewness correction, i.e. one of
`"none"`

, `"1/2"`

, or `"2/3"`

.

- y
Observed number

## Value

Vector of length four with lower and upper bounds of an

\((1-\alpha)\cdot 100\%\) confidence interval (first two
arguments) and corresponding quantile of observation `y`

together with the median of the predictive distribution.