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.
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