5 papers
A tight Hermite-Hadamard's inequality and a generic method for comparison between residuals of inequalities with convex functions
Milan Merkle, Zoran D. Mitrović
We present a tight parametrical Hermite-Hadamard type inequality with probability measure, which yields a considerably closer upper bound for the mean value of convex function than…
On bounds for the mode and median of the generalized hyperbolic and related distributions
Robert E. Gaunt, Milan Merkle
Except for certain parameter values, a closed form formula for the mode of the generalized hyperbolic (GH) distribution is not available. In this paper, we exploit results from the…
Bayesian Approach for Parameter Estimation of Continuous-Time Stochastic Volatility Models using Fourier Transform Methods
Milan Merkle, Yuri F. Saporito, Rodrigo S. Targino
We propose a two stage procedure for the estimation of the parameters of a fairly general, continuous-time stochastic volatility. An important ingredient of the proposed method is…
Approximate Calculation of Tukey's Depth and Median With High-dimensional Data
Milica Bogićević, Milan Merkle
We present a new fast approximate algorithm for Tukey (halfspace) depth level sets and its implementation-ABCDepth. Given a -dimensional data set for any , the algorith…
An axiomatic integral and a multivariate mean value theorem
Milan Merkle
In order to investigate minimal sufficient conditions for an abstract integral to belong to the convex hull of the integrand, we propose a system of axioms under which it happens.…