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Journal articles on the topic 'Log-concavity'

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Author: Grafiati

Published: 18 May 2024

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1

Saumard, Adrien, and Jon A. Wellner. "Log-concavity and strong log-concavity: A review." Statistics Surveys 8 (2014): 45–114. http://dx.doi.org/10.1214/14-ss107.

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2

Llamas, Aurora, and José Martínez-Bernal. "Nested Log-Concavity." Communications in Algebra 38, no. 5 (April 26, 2010): 1968–81. http://dx.doi.org/10.1080/00927870902950662.

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3

Finner, H., and M. Roters. "Distribution functions and log-concavity." Communications in Statistics - Theory and Methods 22, no. 8 (January 1993): 2381–96. http://dx.doi.org/10.1080/03610929308831156.

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4

Wang, Yi. "Linear transformations preserving log-concavity." Linear Algebra and its Applications 359, no. 1-3 (January 2003): 161–67. http://dx.doi.org/10.1016/s0024-3795(02)00438-x.

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5

Lin, Yi, and Álvaro Pelayo. "Log-concavity and symplectic flows." Mathematical Research Letters 22, no. 2 (2015): 501–27. http://dx.doi.org/10.4310/mrl.2015.v22.n2.a9.

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6

Wang, Yi, and Yeong-Nan Yeh. "Log-concavity and LC-positivity." Journal of Combinatorial Theory, Series A 114, no. 2 (February 2007): 195–210. http://dx.doi.org/10.1016/j.jcta.2006.02.001.

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7

Kahn, J., and M. Neiman. "Negative correlation and log-concavity." Random Structures & Algorithms 37, no. 3 (November 30, 2009): 367–88. http://dx.doi.org/10.1002/rsa.20292.

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8

Shaked, Moshe, and J. George Shanthikumar. "Characterization of Some First Passage Times Using Log-Concavity and Log-Convexity as Aging Notions." Probability in the Engineering and Informational Sciences 1, no. 3 (July 1987): 279–91. http://dx.doi.org/10.1017/s026996480000005x.

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An interpretation of log-concavity and log-convexity as aging notions is given in this paper. It imitates a stochastic ordering characterization of the NBU (new better than used) and the NWU (new worse than used) notions but stochastic ordering is now replaced by the likelihood ratio ordering. The new characterization of log-concavity and log-convexity sheds new light on these properties and enables one to obtain intuitively simple proofs of the log-convexity and log-concavity of some first passage times of interest in branching processes and in reliability theory.

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9

Johnson, Oliver, Ioannis Kontoyiannis, and Mokshay Madiman. "Log-concavity, ultra-log-concavity, and a maximum entropy property of discrete compound Poisson measures." Discrete Applied Mathematics 161, no. 9 (June 2013): 1232–50. http://dx.doi.org/10.1016/j.dam.2011.08.025.

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10

Karp, D., and S. M. Sitnik. "Log-convexity and log-concavity of hypergeometric-like functions." Journal of Mathematical Analysis and Applications 364, no. 2 (April 2010): 384–94. http://dx.doi.org/10.1016/j.jmaa.2009.10.057.

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11

Hou, Qing-hu, and Guojie Li. "Log-concavity of P-recursive sequences." Journal of Symbolic Computation 107 (November 2021): 251–68. http://dx.doi.org/10.1016/j.jsc.2021.03.004.

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12

Miravete, Eugenio J. "Preserving Log-Concavity Under Convolution: Comment." Econometrica 70, no. 3 (May 2002): 1253–54. http://dx.doi.org/10.1111/1468-0262.00327.

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13

Lam, Thomas, Alexander Postnikov, and Pavlo Pylyavskyy. "Schur positivity and Schur log-concavity." American Journal of Mathematics 129, no. 6 (2007): 1611–22. http://dx.doi.org/10.1353/ajm.2007.0045.

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14

Johnson, Oliver, and Christina Goldschmidt. "Preservation of log-concavity on summation." ESAIM: Probability and Statistics 10 (April 2006): 206–15. http://dx.doi.org/10.1051/ps:2006008.

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15

Asmussen, Søren, and Jaakko Lehtomaa. "Distinguishing Log-Concavity from Heavy Tails." Risks 5, no. 1 (February 7, 2017): 10. http://dx.doi.org/10.3390/risks5010010.

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16

Chindris, Calin, Harm Derksen, and Jerzy Weyman. "Counterexamples to Okounkov’s log-concavity conjecture." Compositio Mathematica 143, no. 6 (November 2007): 1545–57. http://dx.doi.org/10.1112/s0010437x07003090.

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17

Chen, Huaihou, Hongmei Xie, and Taizhong Hu. "Log-concavity of generalized order statistics." Statistics & Probability Letters 79, no. 3 (February 2009): 396–99. http://dx.doi.org/10.1016/j.spl.2008.09.009.

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18

Hazelton, Martin L. "Assessing log-concavity of multivariate densities." Statistics & Probability Letters 81, no. 1 (January 2011): 121–25. http://dx.doi.org/10.1016/j.spl.2010.10.001.

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19

Mao, Tiantian, Wanwan Xia, and Taizhong Hu. "PRESERVATION OF LOG-CONCAVITY UNDER CONVOLUTION." Probability in the Engineering and Informational Sciences 32, no. 4 (September 26, 2017): 567–79. http://dx.doi.org/10.1017/s0269964817000389.

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Log-concave random variables and their various properties play an increasingly important role in probability, statistics, and other fields. For a distribution F, denote by 𝒟F the set of distributions G such that the convolution of F and G has a log-concave probability mass function or probability density function. In this paper, we investigate sufficient and necessary conditions under which 𝒟F ⊆ 𝒟G, where F and G belong to a parametric family of distributions. Both discrete and continuous settings are considered.

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20

Sagan, Bruce E. "Inductive proofs of q-log concavity." Discrete Mathematics 99, no. 1-3 (April 1992): 289–306. http://dx.doi.org/10.1016/0012-365x(92)90377-r.

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21

Medina, Luis A., and Armin Straub. "On Multiple and Infinite Log-Concavity." Annals of Combinatorics 20, no. 1 (November 2, 2015): 125–38. http://dx.doi.org/10.1007/s00026-015-0292-7.

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22

Bóna, Miklós, Marie-Louise Lackner, and Bruce E. Sagan. "Longest Increasing Subsequences and Log Concavity." Annals of Combinatorics 21, no. 4 (August 19, 2017): 535–49. http://dx.doi.org/10.1007/s00026-017-0365-x.

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23

McNamara, Peter R. W., and Bruce E. Sagan. "Infinite log-concavity: Developments and conjectures." Advances in Applied Mathematics 44, no. 1 (January 2010): 1–15. http://dx.doi.org/10.1016/j.aam.2009.03.001.

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24

Berg, Astrid, Lukas Parapatits, Franz E. Schuster, and Manuel Weberndorfer. "Log-concavity properties of Minkowski valuations." Transactions of the American Mathematical Society 370, no. 7 (March 21, 2018): 5245–77. http://dx.doi.org/10.1090/tran/7434.

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25

DeSalvo, Stephen, and Igor Pak. "Log-concavity of the partition function." Ramanujan Journal 38, no. 1 (August 22, 2014): 61–73. http://dx.doi.org/10.1007/s11139-014-9599-y.

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26

Engel, Benjamin. "Log-concavity of the overpartition function." Ramanujan Journal 43, no. 2 (February 23, 2016): 229–41. http://dx.doi.org/10.1007/s11139-015-9762-0.

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27

Hou, Qing-Hu, and Zuo-Ru Zhang. "r-log-concavity of partition functions." Ramanujan Journal 48, no. 1 (February 15, 2018): 117–29. http://dx.doi.org/10.1007/s11139-017-9975-5.

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28

Schirmacher, Ernesto. "Log-Concavity and the Exponential Formula." Journal of Combinatorial Theory, Series A 85, no. 2 (February 1999): 127–34. http://dx.doi.org/10.1006/jcta.1998.2896.

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29

Li, Shiyue. "Equivariant log-concavity of graph matchings." Algebraic Combinatorics 6, no. 3 (June 19, 2023): 615–22. http://dx.doi.org/10.5802/alco.284.

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30

Xia, Ernest X. W. "On the log-concavity of the sequence for some combinatorial sequences." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148, no. 4 (June 22, 2018): 881–92. http://dx.doi.org/10.1017/s0308210518000033.

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Recently, Sun posed a series of conjectures on the log-concavity of the sequence , where is a familiar combinatorial sequence of positive integers. Luca and Stănică, Hou et al. and Chen et al. proved some of Sun's conjectures. In this paper, we present a criterion on the log-concavity of the sequence . The criterion is based on the existence of a function f(n) that satisfies some inequalities involving terms related to the sequence . Furthermore, we present a heuristic approach to compute f(n). As applications, we prove that, for the Zagier numbers , the sequences are strictly log-concave, which confirms a conjecture of Sun. We also prove the log-concavity of the sequence of Cohen–Rhin numbers.

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31

Ahmia, Moussa, and Hacène Belbachir. "Preserving log-concavity for p,q-binomial coefficient." Discrete Mathematics, Algorithms and Applications 11, no. 02 (April 2019): 1950017. http://dx.doi.org/10.1142/s1793830919500174.

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We study the log-concavity of a sequence of [Formula: see text]-binomial coefficients located on a ray of the [Formula: see text]-Pascal triangle for certain directions, and we establish the preserving log-concavity of linear transformations associated to [Formula: see text]-Pascal triangle.

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32

McCabe, Adam, and Gregory G. Smith. "Log-concavity of asymptotic multigraded Hilbert series." Proceedings of the American Mathematical Society 141, no. 6 (December 20, 2012): 1883–92. http://dx.doi.org/10.1090/s0002-9939-2012-11808-8.

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33

Brenti, Francesco. "Expansions of chromatic polynomials and log-concavity." Transactions of the American Mathematical Society 332, no. 2 (February 1, 1992): 729–56. http://dx.doi.org/10.1090/s0002-9947-1992-1069745-7.

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34

Fang, Rui, and Weiyong Ding. "On relative log-concavity and stochastic comparisons." Statistics & Probability Letters 137 (June 2018): 91–98. http://dx.doi.org/10.1016/j.spl.2018.01.007.

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35

Zhu, Bao-Xuan. "Log-concavity and unimodality of compound polynomials." Discrete Mathematics 313, no. 22 (November 2013): 2602–6. http://dx.doi.org/10.1016/j.disc.2013.08.002.

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36

Kouider, Elies, and Hanfeng Chen. "Concavity of Box-Cox log-likelihood function." Statistics & Probability Letters 25, no. 2 (November 1995): 171–75. http://dx.doi.org/10.1016/0167-7152(94)00219-x.

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37

Kolesnikov, Alexander V. "On Diffusion Semigroups Preserving the Log-Concavity." Journal of Functional Analysis 186, no. 1 (October 2001): 196–205. http://dx.doi.org/10.1006/jfan.2001.3772.

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38

Jakimiuk, Jacek, Daniel Murawski, Piotr Nayar, and Semen Słobodianiuk. "Log-concavity and discrete degrees of freedom." Discrete Mathematics 347, no. 6 (June 2024): 114020. http://dx.doi.org/10.1016/j.disc.2024.114020.

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39

Chen, William Y. C., and Ernest X. W. Xia. "2-Log-Concavity of the Boros–Moll Polynomials." Proceedings of the Edinburgh Mathematical Society 56, no. 3 (August 21, 2013): 701–22. http://dx.doi.org/10.1017/s0013091513000412.

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AbstractThe Boros–Moll polynomialsPm(a)arise in the evaluation of a quartic integral. It has been conjectured by Boros and Moll that these polynomials are infinitely log-concave. In this paper, we show thatPm(a)is 2-log-concave for anym≥ 2. Letdi(m)be the coefficient ofaiinPm(a). We also show that the sequenceis log-concave.

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40

Zhu, Bao-Xuan. "Log-concavity and strong q-log-convexity for Riordan arrays and recursive matrices." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 147, no. 6 (August 14, 2017): 1297–310. http://dx.doi.org/10.1017/s0308210516000500.

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Let [An,k]n,k⩾0 be an infinite lower triangular array satisfying the recurrencefor n ⩾ 1 and k ⩾ 0, where A0,0 = 1, A0,k = Ak,–1 = 0 for k > 0. We present some criteria for the log-concavity of rows and strong q-log-convexity of generating functions of rows. Our results can be applied to many well-known triangular arrays, such as the Pascal triangle, the Stirling triangle of the second kind, the Bell triangle, the large Schröder triangle, the Motzkin triangle, and the Catalan triangles of Aigner and Shapiro, in a unified approach. In addition, we prove that the binomial transformation not only preserves the strong q-log-convexity property, but also preserves the strong q-log-concavity property. Finally, we demonstrate that the strong q-log-convexity property is preserved by the Stirling transformation and Whitney transformation of the second kind, which extends some known results for the strong q-log-convexity property.

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41

Gedefa, Fekadu Tolessa. "Log-Concavity of Centered Polygonal Figurate Number Sequences." OALib 03, no. 06 (2016): 1–5. http://dx.doi.org/10.4236/oalib.1102774.

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42

Stoimenow, Alexander. "LOG-CONCAVITY AND ZEROS OF THE ALEXANDER POLYNOMIAL." Bulletin of the Korean Mathematical Society 51, no. 2 (March 31, 2014): 539–45. http://dx.doi.org/10.4134/bkms.2014.51.2.539.

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43

Yang, Arthur L. B., and James J. Y. Zhao. "Log-concavity of the Fennessey-Larcombe-French Sequence." Taiwanese Journal of Mathematics 20, no. 5 (September 2016): 993–99. http://dx.doi.org/10.11650/tjm.20.2016.6770.

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44

Melbourne, James, and Tomasz Tkocz. "Reversal of Rényi Entropy Inequalities Under Log-Concavity." IEEE Transactions on Information Theory 67, no. 1 (January 2021): 45–51. http://dx.doi.org/10.1109/tit.2020.3024025.

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45

Kauers, Manuel, and Peter Paule. "A Computer Proof of Moll's Log-Concavity Conjecture." Proceedings of the American Mathematical Society 135, no. 12 (December 1, 2007): 3847–57. http://dx.doi.org/10.1090/s0002-9939-07-08912-5.

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46

Mu, Xiaosheng. "Log-concavity of a mixture of beta distributions." Statistics & Probability Letters 99 (April 2015): 125–30. http://dx.doi.org/10.1016/j.spl.2015.01.011.

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47

Brenti, Francesco. "Log-concavity and Combinatorial Properties of Fibonacci Lattices." European Journal of Combinatorics 12, no. 6 (November 1991): 459–76. http://dx.doi.org/10.1016/s0195-6698(13)80097-2.

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48

Sagan, Bruce E. "Inductive and injective proofs of log concavity results." Discrete Mathematics 68, no. 2-3 (1988): 281–92. http://dx.doi.org/10.1016/0012-365x(88)90120-3.

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49

Krattenthaler, Christian. "On theq-log-concavity of Gaussian binomial coefficients." Monatshefte f�r Mathematik 107, no. 4 (December 1989): 333–39. http://dx.doi.org/10.1007/bf01517360.

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50

Butler, Lynne M. "The q-log-concavity of q-binomial coefficients." Journal of Combinatorial Theory, Series A 54, no. 1 (May 1990): 54–63. http://dx.doi.org/10.1016/0097-3165(90)90005-h.

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