# Implements Bivariate POT Method

### Description

Returns an object of class `"gpdbiv"`

representing the fit
of a bivariate POT (peaks over thresholds) model for joint
excesses over thresholds.

### Usage

1 2 |

### Arguments

`data1` |
first data vector |

`data2` |
second data vector |

`u1` |
threshold for |

`u2` |
threshold for |

`ne1` |
number of upper extremes to be used for |

`ne2` |
number of upper extremes to be used for |

`global` |
should a global maximisation of the likelihood with respect to marginal and dependence parameters be undertaken. The default alternative is a two-stage local fit where first the marginal parameters are estimated and then the dependence parameter. This is much faster than a global fit. |

`method` |
the optimization method (see |

`...` |
other arguments passed to |

### Details

This function implements a model suggested by Richard Smith (see references below). The marginal excess distributions are GPD distributions, as suggested by univariate EVT and implemented in gpd. The dependence specification is known as the logistic or Gumbel dependence structure, but it would be easy to program alternatives.

### Value

An object of class `"gpdbiv"`

representing the fit and including
parameter estimates and standard errors.

### References

Multivariate Threshold Methods, Richard L. Smith,
in *Extreme Value Theory and Applications*, ed. J. Galambos,
published by Kluwer, pages 225-248, 1994.

Markov Chain Models for Threshold Exceedances,
R.L. Smith, J.A. Tawn, S.G. Coles,
*Biometrika* **84**, 249-268, 1997.

### See Also

`gpd`

, `plot.gpdbiv`

,
`interpret.gpdbiv`

### Examples

1 2 3 4 |

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