Abstract
In this note we continue the study of gaps in samples of geometric random variables originated in Hitczenko and Knopfmacher [Gap-free compositions and gap-free samples of geometric random variables. Discrete Math. 294 (2005) 225–239] and continued in Louchard and Prodinger [The number of gaps in sequences of geometrically distributed random variables, Preprint available at 〈 http://www.ulb.ac.be/di/mcs/louchard/ 〉 (number 81 on the list) or at 〈 http://math.sun.ac.za/ ∼ prodinger/pdffiles/gapsAPRIL27.pdf. 〉 ] In particular, since the notion of a gap differs in these two papers, we derive some of the results obtained in Louchard and Prodinger [The number of gaps in sequences of geometrically distributed random variables, Preprint available at 〈 http://www.ulb.ac.be/di/mcs/louchard/ 〉 (number 81 on the list) or at 〈 http://math.sun.ac.za/ ∼ prodinger/pdffiles/gapsAPRIL27.pdf. 〉 ] for gaps as defined in Hitczenko and Knopfmacher [Gap-free compositions and gap-free samples of geometric random variables. Discrete Math. 294 (2005) 225–239].
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