Short distances, flat triangles and Poisson limits
- 1 December 1978
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 15 (4), 815-825
- https://doi.org/10.2307/3213436
Abstract
Motivated by problems in the analysis of spatial data, we prove some general Poisson limit theorems for the U-statistics of Hoeffding (1948). The theorems are applied to tests of clustering or collinearities in plane data; nearest neighbour distances are also considered.Keywords
This publication has 12 references indexed in Scilit:
- Rates of Poisson convergence for U-statisticsJournal of Applied Probability, 1979
- Quick tests for spatial interactionBiometrika, 1978
- A Martingale Approach to the Poisson Convergence of Simple Point ProcessesThe Annals of Probability, 1978
- Poisson limits for a clustering model of straussJournal of Applied Probability, 1977
- Two Applications of a Poisson Approximation for Dependent EventsThe Annals of Probability, 1977
- Limit theorems for dissociated random variablesAdvances in Applied Probability, 1976
- Limit theorems for dissociated random variablesAdvances in Applied Probability, 1976
- Characterization and convergence of random measures and point processesProbability Theory and Related Fields, 1973
- Martingale convergence to infinitely divisible laws with finite variancesTransactions of the American Mathematical Society, 1971
- A Class of Statistics with Asymptotically Normal DistributionThe Annals of Mathematical Statistics, 1948