Related papers: Bi-$s^*$-concave distributions
We consider a new class $\boldsymbol{Q}$ of distribution functions $F$ that have the property of rational-infinite divisibility: there exist some infinitely divisible distribution functions $F_1$ and $F_2$ such that $F_1=F*F_2$. A…
Classes of multivariate and cone valued infinitely divisible Gamma distributions are introduced. Particular emphasis is put on the cone-valued case, due to the relevance of infinitely divisible distributions on the positive semi-definite…
In this paper, we introduce a new subclass of harmonic functions $f=s+\overline{t}$ in the open unit disk $U =\left \{ z\in C:\left \vert z\right \vert <1\right \} $ satisfying ${\text{Re}}\left[ \gamma s^{\prime }(z)+\delta zs^{\prime…
We deal with different kinds of generalizations of $\mathcal{S}^*(\psi)$, the class of Ma-Minda starlike functions, in addition to a majorization result of $\mathcal{C}(\psi),$ the class of Ma-Minda convex functions, which are enlisted as…
Kiefer and Wolfowitz [Z. Wahrsch. Verw. Gebiete 34 (1976) 73--85] showed that if $F$ is a strictly curved concave distribution function (corresponding to a strictly monotone density $f$), then the Maximum Likelihood Estimator $\hat{F}_n$,…
In the present paper, the coefficient estimates are found for the class $\mathcal S^{*-1}(\alpha)$ consisting of inverses of functions in the class of univalent starlike functions of order $\alpha$ in $\mathcal D=\{z\in\mathbb C:|z|<1\}$.…
Using a natural representation of a $1/s$-concave function on $\mathbb{R}^d$ as a convex set in $\mathbb{R}^{d+1},$ we derive a simple formula for the integral of its $s$-polar. This leads to convexity properties of the integral of the…
We succeeded to isolate a special class of concave Young-functions enjoying the so-called \emph{density-level property}. In this class there is a proper subset whose members have each the so-called degree of contraction denoted by…
In this paper, we obtained some inequalities for \phi_{s}-convex function, \phi-Godunova-Levin function, \phi-P-function and log-\phi-convex function. Finally, we defined the class of \phi-quasi-convex functions and we examined some…
This article examines the value distribution of $S_{N}(f, \alpha) := \sum_{n=1}^N f(n\alpha)$ for almost every $\alpha$ where $N \in \mathbb{N}$ is ranging over a long interval and $f$ is a $1$-periodic function with discontinuities or…
In this paper, we prove various radius results and obtain sufficient conditions using the convolution for the Ma-Minda classes $\mathcal{S}^*(\psi)$ and $\mathcal{C}(\psi)$ of starlike and convex analytic functions. We also obtain the Bohr…
We study multivariate entire functions and polynomials with non-negative coefficients. A class of {\bf Strongly Log-Concave} entire functions, generalizing {\it Minkowski} volume polynomials, is introduced: an entire function $f$ in $m$…
Properties of four infinite families of special functions of two real variables, based on the compact simple Lie group G2, are compared and described. Two of the four families (called here C- and S-functions) are well known, whereas the…
Let $V$ be a real finite dimensional representation of a compact Lie group $G$. It is well-known that the algebra $\mathbb R[V]^G$ of $G$-invariant polynomials on $V$ is finitely generated, say by $\sigma_1,...,\sigma_p$. Schwarz proved…
Unimodal univariate distributions can be characterized as piecewise convex-concave cumulative distribution functions. In this note we transfer this shape constraint characterization to the quantile function. We show that this…
Set-valued quantiles for multivariate distributions with respect to a general convex cone are introduced which are based on a family of (univariate) distribution functions rather than on the joint distribution function. It is shown that…
For a finite group $G$, we compute the algebraic $K$-theory of the category of equivariant sheaves on a locally compact Hausdorff $G$-space, generalizing a result of Efimov, and determine the equivariant $E$-theory of the $C^*$-algebra of…
The piecewise-concave function may be used to approximate a wide range of other functions to arbitrary precision over a bounded set. In this short paper, this property is proven for three function classes: (a) the multivariate twice…
We derive the strange quark transverse momentum distribution for the $% b\to s\gamma $ decay. A resummed formula is presented showing the singularity structure in the impact parameter $b$. We observe the appearance of a new next-to-leading…
We consider the new class $\boldsymbol{Q}$ of rational-infinitely (or quasi-infinitely) divisible distribution functions on the real line. By definition, $F\in \boldsymbol{Q}$ if there are some infinitely divisible distribution functions…