Exponential–uniform identities related to records
Alexander Marynych (Eindhoven University of Technology)
Abstract
Symmetry properties of the random grid spanned on the set of records from the planar Poisson point process imply bizarre multivariate distributional identities for certain rational functions of independent exponential and uniform random variables.
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Pages: 1-5
Publication Date: July 11, 2012
DOI: 10.1214/ECP.v17-2011
References
- Arratia, Richard; Barbour, A. D.; Tavaré, Simon. A tale of three couplings: Poisson-Dirichlet and GEM approximations for random permutations. Combin. Probab. Comput. 15 (2006), no. 1-2, 31--62. MR2195574
- Baryshnikov, Yu. Supporting-points processes and some of their applications. Probab. Theory Related Fields 117 (2000), no. 2, 163--182. MR1771659
- Dufresne, Daniel. Algebraic properties of beta and gamma distributions, and applications. Adv. in Appl. Math. 20 (1998), no. 3, 285--299. MR1618423
- Gnedin, Alexander V. Best choice from the planar Poisson process. Stochastic Process. Appl. 111 (2004), no. 2, 317--354. MR2056541
- Gnedin, Alexander V. Corners and records of the Poisson process in quadrant. Electron. Commun. Probab. 13 (2008), 187--193. MR2399280
- Goldie, Charles M.; Rogers, L. C. G. The $k$-record processes are i.i.d. Z. Wahrsch. Verw. Gebiete 67 (1984), no. 2, 197--211. MR0758073
- Samuels, Stephen M. Why do these quite different best-choice problems have the same solutions? Adv. in Appl. Probab. 36 (2004), no. 2, 398--416. MR2058142

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