Abstract
The distributions of the mth longest runs of multivariate random sequences are considered. For random sequences made up of k kinds of letters, the lengths of the runs are sorted in two ways to give two definitions of run length ordering. In one definition, the lengths of the runs are sorted separately for each letter type. In the second definition, the lengths of all the runs are sorted together. Exact formulas are developed for the distributions of the mth longest runs for both definitions. The derivations are based on a two-step method that is applicable to various other runs-related distributions, such as joint distributions of several letter types and multiple run lengths of a single letter type.
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This work was supported in part by the Clinical and Translational Science Award UL1 RR024139 from the National Center for Research Resources, National Institutes of Health.
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Kong, Y. The mth longest runs of multivariate random sequences. Ann Inst Stat Math 69, 497–512 (2017). https://doi.org/10.1007/s10463-015-0551-8
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DOI: https://doi.org/10.1007/s10463-015-0551-8