 Fragment size distributions in random fragmentations with cutoffM. Ghorbel and T. Huillet Statistics & Probability Letters, 2005, vol. 71, issue 1, 47-60 Abstract: We consider the following fragmentation model with cutoff: a fragment with initial size x0>1 splits into b>1 daughter fragments with random sizes, the partition law of which has exchangeable distribution. In subsequent steps, fragmentation proceeds independently for each sub-fragments whose sizes are bigger than some cutoff value xc=1 only. This process naturally terminates with probability 1. The size of a fragment is the random mass attached to a leaf of a "typical" path of the full (finite) fragmentation tree. The height's law of typical paths is first analyzed, using analytic and renewal processes techniques. We then compute fragments' size limiting distribution (x0[short up arrow][infinity]), for various senses of a typical path. Next, we exhibit some of its statistical features, essentially in the case of the exchangeable Dirichlet partition model. Keywords: Fragmentation; models; Random; partitions (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:71:y:2005:i:1:p:47-60 Ordering information: This journal article can be ordered from Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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