Graphical characterisation of probability distribution tails |
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| Authors: | K Chaouche P Hubert G Lang |
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| Institution: | (1) Laboratoire GRESE, ENGREF, 19, avenue du Maine, 75732 Paris Cedex 15, France e-mail: lang@engref.fr, FR;(2) UMR Sisyphe, Ecole des Mines de Paris, 35, rue St Honoré, 77305 Fontainebleau, France, FR |
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| Abstract: | The purpose of this paper is to present a graphical method to characterise the nature of a distribution (exponential or algebraic).
In the algebraic case, this statistical tool provides an estimation procedure of the parameter characterising the decrease
of the survival function. The realizations of the random variable under study being available in the form of time series,
this method is based on the relationship between the duration of exceeding an intensity threshold and the accumulation of
the realizations of the random variable during this length of time. The behaviour of the duration-accumulation graphs (when
the threshold of reference increases indefinitely) results in a function, the limit of which only depends on the parameter
characterising the algebraic decrease of the probability distribution. The estimate of this parameter is biased but can be
corrected effectively by numerical methods. We applied this method to two rainfall series differing by their geographical
origin (Dédougou in Burkina Faso and a station on the Island of La Réunion) and their time step (respectively 1 day and 76
seconds). For both of them, the behaviour of tail distributions is shown to be algebraic and the values of the parameter characterizing
the algebraic decrease of the probability distribution of the two series are very close. This would tend to justify the assumption
of a multifractal nature for these series.
This work was achieved as part of the National Programme of Research in Hydrology of the INSU (project 99 PNRH 27). The authors
are grateful to A. Barcello for providing them the data of the Island of La Réunion Island. |
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| Keywords: | : Rainfall extremes Pareto distribution Scale invariance |
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