Monotone additive statistics

02/01/2021

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We study statistics: mappings from distributions to real numbers. We characterize all statistics that are monotone with respect to first-order stochastic dominance, and additive for sums of independent random variables. We explore a number of applications, including a representation of stationary, monotone time preferences, generalizing Fishburn and Rubinstein (1982) to time lotteries.

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Monotone additive statistics

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Monotone additive statistics

Related Research

Stochastic monotonicity and the Markov product for copulas

Altitude Terrain Guarding and Guarding Uni-Monotone Polygons

Comparisons of Order Statistics from Some Heterogeneous Discrete Distributions

A unified approach to explicit formulae for the distributions of runs

Infinitely exchangeable random graphs generated from a Poisson point process on monotone sets and applications to cluster analysis for networks

When is an automatic set an additive basis?

Erdős-Selfridge Theorem for Nonmonotone CNFs