Limit laws for the diameter of a set of random points from a distribution supported by a smoothly bounded set
| Autor: | Michael Schrempp |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Limit of a function Bounded set media_common.quotation_subject Economics Econometrics and Finance (miscellaneous) Boundary (topology) Poisson distribution 01 natural sciences Set (abstract data type) 010104 statistics & probability symbols.namesake 0502 economics and business FOS: Mathematics 050207 economics 0101 mathematics Engineering (miscellaneous) Mathematics media_common Probability (math.PR) 05 social sciences Mathematical analysis Infinity Ellipsoid Distribution (mathematics) symbols Mathematics - Probability |
| Zdroj: | Extremes. 22:167-191 |
| ISSN: | 1572-915X 1386-1999 |
| DOI: | 10.1007/s10687-018-0309-9 |
| Popis: | We study the asymptotic behavior of the maximum interpoint distance of random points in a $d$-dimensional set with a unique diameter and a smooth boundary at the poles. Instead of investigating only a fixed number of $n$ points as $n$ tends to infinity, we consider the much more general setting in which the random points are the supports of appropriately defined Poisson processes. The main result covers the case of uniformly distributed points within a $d$-dimensional ellipsoid with a unique major axis. Moreover, several generalizations of the main result are established, for example a limit law for the maximum interpoint distance of random points from a Pearson type II distribution. |
| Databáze: | OpenAIRE |
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