# Wave:AnnualRecurrenceProbability

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This analysis method calculates the annual recurrence probility and the return period of annual maxima using the Weibull^{[1]} plotting position method.

First, the maximum value in each hydrological year is determined. The probability of recurrence and the return period are then calculated using the following formulas:

[math]\displaystyle{ P = \frac{m}{n+1} }[/math]

and

[math]\displaystyle{ T = \frac{1}{P} }[/math]

where

`m`

: ordered rank of the event (1 = largest event)`n`

: number of total events/years`P`

: probability of exceedance [-]`T`

: return period [years]

The analysis results are a result table with all events and their properties, a result chart plotting the return periods and a result series in the main chart containing only the annual maxima.

## Notes

- If two or more events have the same maximum value, they are assigned the same rank and thus have the same recurrence probability

## Literature

- ↑
**Weibull. W.**(1939): A statistical theory of strength of materials. Ingeniorsvetenskapsakademiens Handlingar, 151, 1–45