%0 Generic %1 pitman2012biased %A Pitman, Jim %A Tran, Ngoc Mai %D 2012 %K biased distributed identically independent permutation sequence size %T Size biased permutation of a finite sequence with independent and identically distributed terms %U http://arxiv.org/abs/1210.7856 %X This paper focuses on the size-biased permutation of $n$ independent and identically distributed (i.i.d) positive random variables. Our setting is a finite dimensional analogue of the size-biased permutation of ranked jumps of a subordinator studied in Perman-Pitman-Yor, as well as a special form of induced order statistics. This intersection grants us different tools for deriving distributional properties. Their comparisons lead to new results, as well as simpler proofs of existing ones. Our main contribution, Theorem 19 in Section 5, describes the asymptotic distribution of the last few terms in a finite i.i.d size-biased permutation via a Poisson coupling with its few smallest order statistics.

@misc{pitman2012biased, abstract = {This paper focuses on the size-biased permutation of $n$ independent and identically distributed (i.i.d) positive random variables. Our setting is a finite dimensional analogue of the size-biased permutation of ranked jumps of a subordinator studied in Perman-Pitman-Yor, as well as a special form of induced order statistics. This intersection grants us different tools for deriving distributional properties. Their comparisons lead to new results, as well as simpler proofs of existing ones. Our main contribution, Theorem 19 in Section 5, describes the asymptotic distribution of the last few terms in a finite i.i.d size-biased permutation via a Poisson coupling with its few smallest order statistics.}, added-at = {2012-11-03T20:44:29.000+0100}, author = {Pitman, Jim and Tran, Ngoc Mai}, biburl = {https://www.bibsonomy.org/bibtex/25b44c98bf52e58bf48cd9134132551b1/pitman}, description = {[1210.7856] Size biased permutation of a finite sequence with independent and identically distributed terms}, interhash = {1f8f438126e04e8d5f8f1207d58f1b14}, intrahash = {5b44c98bf52e58bf48cd9134132551b1}, keywords = {biased distributed identically independent permutation sequence size}, note = {cite arxiv:1210.7856 Comment: 19 pages, 1 figure}, timestamp = {2012-11-03T20:44:29.000+0100}, title = {Size biased permutation of a finite sequence with independent and identically distributed terms}, url = {http://arxiv.org/abs/1210.7856}, year = 2012 }