Access the full text.
Sign up today, get DeepDyve free for 14 days.
(2011)
Convexity, vol. 187 of Cambridge Tracts in Mathematics
e-mail: jaw@stat.washington
J. Doob (1953)
Stochastic processes
(1968)
Total positivity
T. Liggett (1997)
Ultra Logconcave Sequences and Negative DependenceJ. Comb. Theory, Ser. A, 79
(2011)
A strong log-concavity property
F. Balabdaoui, J. Wellner (2012)
Chernoff's density is log-concave.Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, 20 1
J. Cooper (1970)
TOTAL POSITIVITY, VOL. IBulletin of The London Mathematical Society, 2
Gilles Hargé (2004)
A convex/log-concave correlation inequality for Gaussian measure and an application to abstract Wiener spacesProbability Theory and Related Fields, 130
W. Whitt (1985)
Uniform conditional variability ordering of probability distributionsJournal of Applied Probability, 22
(1982)
A proof of the central limit theorem motivated by the Cramér - Rao inequality
G. Burton (2004)
TOPICS IN OPTIMAL TRANSPORTATION (Graduate Studies in Mathematics 58) By CÉDRIC VILLANI: 370 pp., US$59.00, ISBN 0-8218-3312-X (American Mathematical Society, Providence, RI, 2003)Bulletin of The London Mathematical Society, 36
B. Efron (1965)
Increasing Properties of Polya Frequency FunctionAnnals of Mathematical Statistics, 36
(2003)
Topics in optimal transportation, vol
(1982)
A proof of the central limit theorem motivated by the Cramér-Rao inequality. In Statistics and probability: essays in honor of C
L. Shepp, I. Olkin (1981)
Entropy of the Sum of Independent Bernoulli Random Variables and of the Multinomial Distribution
P. Harremoës (2001)
Binomial and Poisson distributions as maximum entropy distributionsIEEE Trans. Inf. Theory, 47
L. Caffarelli (2000)
Monotonicity Properties of Optimal Transportation¶and the FKG and Related InequalitiesCommunications in Mathematical Physics, 214
W. McCormick, J. Gani, V. Rohatgi (1984)
Contributions to Probability.Journal of the American Statistical Association, 79
O. Johnson (2006)
Log-concavity and the maximum entropy property of the Poisson distributionStochastic Processes and their Applications, 117
E. Carlen, A. Soffer (1991)
Entropy production by block variable summation and central limit theoremsCommunications in Mathematical Physics, 140
W. Ehm (1991)
Binomial approximation to the Poisson binomial distributionStatistics & Probability Letters, 11
O. Johnson, Ioannis Kontoyiannis, M. Madiman (2009)
Log-concavity, ultra-log-concavity, and a maximum entropy property of discrete compound Poisson measuresArXiv, abs/0912.0581
P. Nayar, K. Oleszkiewicz (2012)
Khinchine type inequalities with optimal constants via ultra log-concavityPositivity, 16
C. Villani (2003)
Topics in Optimal Transportation
(2003)
Topics in optimal transportation, vol. 58 of Graduate Studies in Mathematics
L. Gurvits (2009)
A Short Proof, Based on Mixed Volumes, of Liggett's Theorem on the Convolution of Ultra-Logconcave SequencesElectron. J. Comb., 16
(2012)
Khinchine type inequalities with
O. Johnson, A. Barron (2001)
Fisher information inequalities and the central limit theoremProbability Theory and Related Fields, 129
J. Kahn, Michael Neiman (2009)
A strong log-concavity property for measures on Boolean algebrasJ. Comb. Theory, Ser. A, 118
Bastian Goldlücke (2014)
Variational Analysis
Ioannis Kontoyiannis, P. Harremoës, O. Johnson (2002)
Entropy and the law of small numbersIEEE Transactions on Information Theory, 51
A. Barron (1986)
ENTROPY AND THE CENTRAL LIMIT THEOREMAnnals of Probability, 14
[We review and formulate results concerning strong-log-concavity in both discrete and continuous settings. Although four different proofs of preservation of strong log-concavity are known in the discrete setting (where strong log-concavity is known as “ultra-log-concavity”), preservation of strong logconcavity under convolution has apparently not been investigated previously in the continuous case.]
Published: Apr 1, 2013
Keywords: Log-concave; ultra log-concave; strongly log-concave; convolution.
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.