# Index Confidence Interval

`ICI.Rd`

The MP adjusts catch based on the value of the index in the current year relative to the time series mean and standard error.

## Arguments

- x
A position in the data object

- Data
A data object

- reps
The number of stochastic samples of the MP recommendation(s)

- plot
Logical. Show the plot?

## Value

An object of class `Rec-class`

with the `TAC`

slot populated with a numeric vector of length `reps`

## Details

The TAC is calculated as:
$$\textrm{TAC}_y=C_{y-1} \alpha$$
where \(C_{y-1}\) is the catch from the previous year, and \(\alpha\) is
defined as:
$$\alpha =
\left\{\begin{array}{ll}
d & \textrm{if } I < \textrm{CI}_L \\
u & \textrm{if } I > \textrm{CI}_H \\
1 & \textrm{if } \textrm{CI}_L \leq I \leq \textrm{CI}_H \\
\end{array}\right.
$$
where \(I\) is the index in the most recent year, \(d\) is 0.75 for `ICI`

and `ICI2`

,
\(u\) is 1.05 and 1.25 for`ICI`

and `ICI2`

respectively, and \(\textrm{CI}_L\)
and \(\textrm{CI}_L\) are the lower and upper bound of the confidence
interval of mean historical index. The confidence interval is
calculated using Z-scores described in the Functions section below.

## Functions

`ICI`

: The catch is reduced by 0.75 if the Z-score of the current year's index is less than -0.44. The catch is increased by 1.05 if the Z-score of the current year's index is greater than 1.96. Otherwise, the catch is held constant.`ICI2`

: This method is less precautionary of the two ICI MPs by allowing for a larger increase in TAC and a lower threshold of the index to decrease the TAC. The catch is reduced by 0.75 if the Z-score of the current year's index is less than -1.96. The catch is increased by 1.25 if the Z-score of the current year's index is greater than 1.96. Otherwise, the catch is held constant.

## Rendered Equations

See Online Documentation for correctly rendered equations

## References

Ernesto Jardim, Manuela Azevedo, Nuno M. Brites, Harvest control rules for data limited stocks using length-based reference points and survey biomass indices, Fisheries Research, Volume 171, November 2015, Pages 12-19, ISSN 0165-7836, https://doi.org/10.1016/j.fishres.2014.11.013

## Examples

```
ICI(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)
#> TAC (median)
#> 13.79784
ICI2(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)
#> TAC (median)
#> 13.60642
```