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Schollmeyer, Georg (31. August 2017): Lower quantiles for complete lattices. Department of Statistics: Technical Reports, No.207 [PDF, 528kB]

Abstract

In this technical report a notion of (lower) quantiles for data or random variables with values in a complete lattice is developed. We list a number of desirable properties a reasonable notion of quantiles should have and analyze for different proposals of quantiles, which of these properties they fulfill. It turns out that one of the constructions has acceptable properties and can thus be used for analyzing lattice-valued data.

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