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Log-Concavity and Strong Log-Concavity: a review. [PDF]
Stat Surv, 2014 We review and formulate results concerning log-concavity and strong-log-concavity in both discrete and continuous settings. We show how preservation of log-concavity and strongly log-concavity on $\mathbb{R}$ under convolution follows from a fundamental ...
Saumard A, Wellner JA.
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Log concavity for unimodal sequences. [PDF]
Res Number Theory, 2023 AbstractIn this paper, we prove that the number of unimodal sequences of size n is log-concave. These are coefficients of a mixed false modular form and have a Rademacher-type exact formula due to recent work of the second author and Nazaroglu on false theta functions.
Bridges W, Bringmann K.
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Skew log-concavity of the Boros-Moll sequences [PDF]
Journal of Inequalities and Applications, 2017 Let { T ( n , k ) } 0 ≤ n < ∞ , 0 ≤ k ≤ n $\{T(n,k)\}_{0\leq n < \infty, 0\leq k \leq n} $ be a triangular array of numbers. We say that T ( n , k ) $T(n,k)$ is skew log-concave if for any fixed n, the sequence { T ( n + k , k ) } 0 ≤ k < ∞ $\{T(n+k,k ...
Eric H Liu
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Distinguishing Log-Concavity from Heavy Tails [PDF]
Risks, 2017 Well-behaved densities are typically log-convex with heavy tails and log-concave with light ones. We discuss a benchmark for distinguishing between the two cases, based on the observation that large values of a sum X 1 + X 2 occur as result ...
Søren Asmussen, Jaakko Lehtomaa
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Infinite log-concavity: developments and conjectures [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Given a sequence $(a_k)=a_0,a_1,a_2,\ldots$ of real numbers, define a new sequence $\mathcal{L}(a_k)=(b_k)$ where $b_k=a_k^2-a_{k-1}a_{k+1}$. So $(a_k)$ is log-concave if and only if $(b_k)$ is a nonnegative sequence. Call $(a_k)$ $\textit{infinitely log-
Peter R. W. McNamara, Bruce E. Sagan
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Horizontal and vertical log-concavity [PDF]
Research in Number Theory, 2021 AbstractHorizontal and vertical generating functions and recursion relations have been investigated by Comtet for triangular double sequences. In this paper we investigate the horizontal and vertical log-concavity of triangular sequences assigned to polynomials which show up in combinatorics, number theory and physics.
Heim, Bernhard, Neuhauser, Markus
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Log-concavity of P-recursive sequences [PDF]
Journal of Symbolic Computation, 2021 We consider the higher order Turán inequality and higher order log-concavity for sequences $\{a_n\}_{n \ge 0}$ such that \[ \frac{a_{n-1}a_{n+1}}{a_n^2} = 1 + \sum_{i=1}^m \frac{r_i(\log n)}{n^{α_i}} + o\left( \frac{1}{n^β} \right), \] where $m$ is a nonnegative integer, $α_i$ are real numbers, $r_i(x)$ are rational functions of $x$ and \[ 0 < α_1 ...
Hou, Qing-hu, Li, Guojie
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Bi-log-concave distribution functions [PDF]
Journal of Statistical Planning and Inference, 2017 Nonparametric statistics for distribution functions F or densities f=F' under qualitative shape constraints provides an interesting alternative to classical parametric or entirely nonparametric approaches. We contribute to this area by considering a new shape constraint: F is said to be bi-log-concave, if both log(F) and log(1 - F) are concave.
Dümbgen Lutz +2 more
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Refined ratio monotonicity of the coordinator polynomials of the root lattice of type Bn
Open Mathematics, 2023 Ratio monotonicity, a property stronger than both log-concavity and the spiral property, describes the behavior of the coefficients of many classical polynomials.
Su Xun-Tuan, Sun Fan-Bo
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Some Inequalities of Extended Hypergeometric Functions
Mathematics, 2021 Hypergeometric functions and their inequalities have found frequent applications in various fields of mathematical sciences. Motivated by the above, we set up certain inequalities including extended type Gauss hypergeometric function and confluent ...
Shilpi Jain +3 more
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