Size bias for one and all

DOI10.1214/13-PS221zbMath1427.60002arXiv1308.2729OpenAlexW2963310951MaRDI QIDQ1755506

Larry Goldstein, Richard Arratia, Fred Kochman

Publication date: 10 January 2019

Published in: Probability Surveys (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.2729

zbMATH Keywords

Stein's methodtightnessbias

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Probability distributions: general theory (60E05) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Research exposition (monographs, survey articles) pertaining to probability theory (60-02)

Related Items (27)

A complement to the Chebyshev integral inequality ⋮ Geometric sums, size biasing and zero biasing ⋮ Conditional tail expectation decomposition and conditional mean risk sharing for dependent and conditionally independent losses ⋮ Statistical aspects of the quantum supremacy demonstration ⋮ Concentration inequalities from monotone couplings for graphs, walks, trees and branching processes ⋮ Can a regulatory risk measure induce profit-maximizing risk capital allocations? The case of conditional tail expectation ⋮ Gamma, Gaussian and Poisson approximations for random sums using size-biased and generalized zero-biased couplings ⋮ From risk reduction to risk elimination by conditional mean risk sharing of independent losses ⋮ Approaching the coupon collector’s problem with group drawings via Stein’s method ⋮ On the second eigenvalue of random bipartite biregular graphs ⋮ Card guessing and the birthday problem for sampling without replacement ⋮ Particle density in diffusion-limited annihilating systems ⋮ Stereological determination of particle size distributions for similar convex bodies ⋮ Pólya urns with immigration at random times ⋮ Indetermined Moment Problems Related to $q$-Functional Equations ⋮ Bounded size bias coupling: a gamma function bound, and universal Dickman-function behavior ⋮ Non uniform exponential bounds on normal approximation by Stein’s method and monotone size bias couplings ⋮ Size biased couplings and the spectral gap for random regular graphs ⋮ Bounded size biased couplings, log concave distributions and concentration of measure for occupancy models ⋮ Distributional transformations without orthogonality relations ⋮ Faces in random great hypersphere tessellations ⋮ SIZE-BIASED TRANSFORM AND CONDITIONAL MEAN RISK SHARING, WITH APPLICATION TO P2P INSURANCE AND TONTINES ⋮ Size-Biased Risk Measures of Compound Sums ⋮ Poisson approximation with applications to stochastic geometry ⋮ On local weak limit and subgraph counts for sparse random graphs ⋮ Discussion on “Size-Biased Risk Measures of Compound Sums,” by Michel Denuit, January 2020 ⋮ Reply to Edward Furman, Yisub Kye, and Jianxi Su on Their Discussion on the Paper Titled “Size-Biased Risk Measures of Compound Sums”

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