scholarly journals Logarithmic concavity, unitarity and selfadjointness

2005 ◽  
Author(s):  
Jan Stochel
Keyword(s):  
Logarithmic Concavity

Logarithmic concavity of the inverse incomplete beta function with respect to the first parameter

2021 ◽  
Vol 127 (1) ◽  
pp. 111-130
Author(s):  
Dimitris Askitis
Keyword(s):  
Distribution Function ◽  
Beta Distribution ◽  
Probability Distributions ◽  
Beta Function ◽  
Incomplete Beta Function ◽  
Univariate Function ◽  
Convexity Properties ◽  
Logarithmic Concavity ◽  
Two Parameter ◽  
Monotonicity Results

The beta distribution is a two-parameter family of probability distributions whose distribution function is the (regularised) incomplete beta function. In this paper, the inverse incomplete beta function is studied analytically as a univariate function of the first parameter. Monotonicity, limit results and convexity properties are provided. In particular, logarithmic concavity of the inverse incomplete beta function is established. In addition, we provide monotonicity results on inverses of a larger class of parametrised distributions that may be of independent interest.

scholarly journals Subsequence numbers and logarithmic concavity

1976 ◽  
Vol 16 (2) ◽  
pp. 123-140 ◽  
Author(s):  
P.J. Chase
Keyword(s):  
Logarithmic Concavity

scholarly journals Logarithmic concavity of series in gamma ratios

2014 ◽  
Vol 58 (6) ◽  
pp. 63-68 ◽  
Author(s):  
S. I. Kalmykov ◽  
D. B. Karp
Keyword(s):  
Logarithmic Concavity

scholarly journals Matroid Inequalities from Electrical Network Theory

10.37236/1893 ◽  
2005 ◽  
Vol 11 (2) ◽  
Author(s):  
David G. Wagner
Keyword(s):  
Half Plane ◽  
Network Theory ◽  
Electrical Network ◽  
Logarithmic Concavity

In 1981, Stanley applied the Aleksandrov–Fenchel Inequalities to prove a logarithmic concavity theorem for regular matroids. Using ideas from electrical network theory we prove a generalization of this for the wider class of matroids with the "half–plane property". Then we explore a nest of inequalities for weighted basis–generating polynomials that are related to these ideas. As a first result from this investigation we find that every matroid of rank three or corank three satisfies a condition only slightly weaker than the conclusion of Stanley's theorem.

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