We extend Hoggar’s result that the sum of two independent discrete-valued log-concave random variables is itself log-concave. Firstly, we weaken the assumption of independence, and introduce conditions under which the result still holds for dependent variables. Secondly, we introduce a wider class of random variables such that in the independent case the sum is still log-concave, and prove simp...

In this note, we study the n×n random Euclidean matrix whose entry (i, j) is equal to f(‖Xi−Xj‖) for some function f and the Xi’s are i.i.d. isotropic vectors inR. In the regime where n and p both grow to infinity and are proportional, we give some sufficient conditions for the empirical distribution of the eigenvalues to converge weakly. We illustrate our result on log-concave random vectors.

We calculate genus distribution formulas for several families of ring-like graphs and prove that they are log-concave. The graphs in each of our ring-like families are obtained by applying the self-bar-amalgamation operation to the graphs in a linear family (linear in the sense of Stahl). That is, we join the two root-vertices of each graph in the linear family. Although log-concavity has been ...

We consider a novel sub-class of log-location-scale models for survival and reliability data formed by restricting the density of the underlying location-scale distribution to be log-concave. These models display a number of attractive properties. We particularly explore the shapes of the hazard functions of these, LLSLC, models. A relatively elegant, if partial, theory of hazard shape arises u...

In this manuscript, a new class of extended (m1,m2)-convex and concave functions is introduced. After some properties of (m1,m2)-convex functions have been given, the inequalities obtained with Hölder and Hölder-İşcan and power-mean and improwed power-mean integral inequalities have been compared and it has been shown that the inequality with Hölder-İşcan inequality gives a better approach than...

the aim of this paper is to prove some inequalities for p-valent meromorphic functions in thepunctured unit disk δ* and find important corollaries.

Hyperbolic polynomials have their origins in partial diierential equations. We show in this paper that they have applications in interior point methods for convex programming. Each homogeneous hyperbolic polynomial p has an associated open and convex cone called its hyperbolicity cone. We give an explicit representation of this cone in terms of polynomial inequalities. The function F (x) = ? lo...

the rational cubic function with three parameters has been extended to rational bi-cubic function to visualize the shape of regular convex surface data. the rational bi-cubic function involves six parameters in each rectangular patch. data dependent constraints are derived on four of these parameters to visualize the shape of convex surface data while other two are free to refine the shape of s...