### Abstract

In the peak over threshold model resulting in the Extreme-value distribution, type I, (EV1) the first e of the distribution function is based on the Poisson number of exceedances, and the second e arises from the Exponentially distributed magnitudes. This paper, on the one hand, generalises the Poisson model to the (positive and negative) Binomial distribution, and, on the other hand, the Exponential distribution is generalised to the Generalised Pareto distribution. Lack of fit with respect to the Poisson and Exponential distribution is measured by statistics derived from those which would be locally most powerful if the estimates of the location and scale parameter were equal to the true parameter values. Ways of combining both statistics are discussed.

Original language | English |
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Pages (from-to) | 69-76 |

Journal | Stochastic hydrology and hydraulics |

Volume | 5 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1991 |

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## Cite this

van Montfort, M. A. J., & Otten, A. (1991). The first and second e of the extreme value distribution.

*Stochastic hydrology and hydraulics*,*5*(1), 69-76. https://doi.org/10.1007/BF01544179