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The two-dimensional Poisson process and extremal processes

1971; Cambridge University Press; Volume: 8; Issue: 4 Linguagem: Inglês

10.2307/3212238

1475-6072

James Pickands,

Statistical Distribution Estimation and Applications

In recent years many applications of probability theory have involved such concepts as records, inter-record times and extreme order statistics. The results have generally been proved by diverse methods. In the present work a unifying structure is presented, which makes possible the simplification and extension of some of these results. The approach taken is to place all relevant processes on the same sample space. The underlying sample space is a homogeneous two-dimensional Poisson process.