Log-concave probability and its applications

By Mark Bagnoli, Ted Bergstrom. 2004

1,636 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/2f02f2072717353378ada9a486729936f288ab2b

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In Artificial Intelligence

Citations in the corpus

Why does democracy need education? (2007, neutral): “Bagnoli and Bergstrom (1989) show that this assumption is satisfied by the uniform, normal, lognormal, exponential, Pareto, logistic, gamma, chi-square, extreme-value, power-function, Weibull and Laplace distributions, and by any truncation thereof.”
The Agency Model and MFN Clauses (2017, background): “As shown by Bagnoli and Bergstrom (2005), many common distributions generate demand that is logconcave or log-convex.”
Competing Environmental Labels (2014, background): “…which is defined as f (φ; a , b) = φ a−1(1 − φ)b−1∫ 1 0 u a−1(1 − u)b−1du = (a + b) (a ) (b) φa−1(1 − φ)b−1, where (u) is the gamma function.9 The Beta distribution is defined on the interval [0, 1], has mean E(φ) = a/(a + b), and is log-concave if a ≥ 1 and b ≥ 1 (Bagnoli and Bergstrom 2005).”
An Elementary Theory of Comparative Advantage (2009, neutral): “Like log-supermodularity, log-concavity is satis ed by many standard distributions including the uniform, normal, and extreme value distributions; see Bergstrom and Bagnoli (2005).”
To bundle or not to bundle (2006, methodology): “We thank Mark Armstrong, Ted Bergstrom, Larry Samuelson, Bill Sandholm, Ananth Seshadri, and Stephen Morris for comments and helpful discussions.”
Maximum likelihood estimation of a multi‐dimensional log‐concave density (2008, background): “α,β/ distributions with α,β 1, Weibull distributions with shape parameter at least 1, Gumbel, logistic and Laplace densities; see Bagnoli and Bergstrom (2005) for other examples.”
Discriminatory Information Disclosure (2017, neutral): “The buyer’s ex ante type θ is uniformly distributed, with distribution function Φ(θ) = 2θ − 1 and support [ 1 2 , 1 ] .”
Efficient Robust Proper Learning of Log-concave Distributions (2016, background): “In the continuous setting, they include uniform, normal, exponential, logistic, extreme value, Laplace, Weibull, Gamma, Chi and Chi-Squared and Beta distributions (see [BB05]).”
Geometrically concave univariate distributions (2010, background): “(a) The proof of parts (a) and (b) of Theorem 2 is given in [5,6].”
Portfolio diversification and value at risk under thick-tailedness (2009, background): “X with density f(x), x2R, and the convex distribution support ¼ {x2R : f(x)40} is log-concavely distributed if log f(x) is concave in x2 , that is, if for all x1, x22 , and any 2 [0, 1], f( x1þ (1 )x2) ( f(x1)) ( f(x2))1 (see An 1998, Bagnoli and Bergstrom 2005).”
Job Referral Networks and the Determination of Earnings in Local Labor Markets (2014, neutral): “1− F(ψ̃) < (1− q)(1− F(ψ̃0)) 1− ( q + (1− q) F(ψ̃0) ) < (1− q)(1− F(ψ̃0)) (1− q)(1− F(ψ̃0)) < (1− q)(1− F(ψ̃0)), (23)For details on log concave functions and their application to search models, see Bagnoli and Bergstrom (2005) and Flinn and Heckman (1983).”
New Results Concerning Probability Distributions with Increasing Generalized Failure Rates (2012, neutral): “Finally, we analyze all common (continuous and discrete) distributions for the prevalence of the IGFR property, and derive and tabulate their generalized failure rates, for future reference.”
Cash Holdings and Credit Risk (2012, neutral): “Bagnoli and Bergstrom (2005) show that the hazard rate is weakly monotonic if the function (1−G(u)) is log-concave, which holds for uniform, normal, logistic, exponential, and many other probability distributions.”