Note

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# Estimate tail dependence coefficients on the wind dataΒΆ

In this example we estimate the tail dependence coefficient of a bivariate sample applied to the corresponding annual maximum wind speeds over the period 1944-1983 at two locations in the United States: Albany, New-York and Hartford, Connecticut. Readers should refer to [coles2001] to get more details.

First, we load the wave_surge dataset. The speeds are expressed in knot : one knot is equalt to one nautical mile per hour, which means .

```
import openturns as ot
import openturns.viewer as otv
from openturns.usecases import coles
data = coles.Coles().wind[:, 1:]
print(data[:5])
graph = ot.Graph(
"Annual maximum wind speeds at Albany (NY) and Hartford (CT)", "spped at Albany (knot)", "speed at Hartford (knot)", True, ""
)
cloud = ot.Cloud(data)
cloud.setColor("red")
graph.add(cloud)
view = otv.View(graph)
```

```
[ Hartford Albany ]
0 : [ 49 52 ]
1 : [ 54 46 ]
2 : [ 60 48 ]
3 : [ 49 44 ]
4 : [ 57 42 ]
```

We plot the graph of the function and the graph of the function . We conclude that both variables are asymptotially dependent as and that they are positively correlated as . We cn visually deduce the upper tail dependence coefficient and the upper extremal dependence coefficient . Note that the number of data points is so small that the curves seem chaotic. It is difficult, if not impossible, to deduce the value of and from the curves.

```
graph1 = ot.VisualTest.DrawUpperTailDependenceFunction(data)
graph2 = ot.VisualTest.DrawUpperExtremalDependenceFunction(data)
grid = ot.GridLayout(1, 2)
grid.setGraph(0, 0, graph1)
grid.setGraph(0, 1, graph2)
view = otv.View(grid)
```

```
otv.View.ShowAll()
```