Location- and scale-free procedures for distinguishing between distribution tail models

We consider distinguishing between two distribution tail models when tails of one model are lighter (or heavier) than those of the other. Two procedures are proposed: one scale-free and one location- and scale-free, and their asymptotic properties are established. We show the advantage of using these procedures for distinguishing between certain tail models in comparison with the tests proposed in the literature by simulation and apply them to data on daily precipitation in Green Bay, US and Saentis, Switzerland

Censored extreme value estimation

A novel and comprehensive methodology designed to tackle the challenges posed by extreme values in the context of random censorship is introduced. The main focus is on the analysis of integrals based on the product-limit estimator of normalized upper order statistics, called extreme Kaplan--Meier integrals. These integrals allow for the transparent derivation of various important asymptotic distributional properties, offering an alternative approach to conventional plug-in estimation methods. Notably, this methodology demonstrates robustness and wide applicability within the scope of max-domains of attraction. A noteworthy by-product is the extension of generalized Hill-type estimators of extremes to encompass all max-domains of attraction, which is of independent interest. The theoretical framework is applied to construct novel estimators for positive and real-valued extreme value indices for right-censored data. Simulation studies supporting the theory are provided

Precise large deviations for dependent subexponential variables

In this paper we study precise large deviations for the partial sums of a stationary sequence with a subexponential marginal distribution. Our main focus is on distributions which either have a regularly varying or a lognormal-type tail. We apply the results to prove limit theory for the maxima of the entries large sample covariance matrices

The distribution of the maximum number of common neighbors in the random graph

Let $\Delta_{k;n}$ be the maximum number of common neighbors of a set of $k$ vertices in $G(n,p)$. In this paper, we find $a_n$ and $\sigma_n$ such that $\frac{\Delta_{k;n}-a_n}{\sigma_n}$ converges in distribution to a random variable having the standard Gumbel distribution

The Comparison of Direct and Indirect Methods for Determining the Magnetocaloric Parameters in the Heusler Alloy Ni50Mn34.8In14.2B

The magnetocaloric properties of the Ni50Mn34.8In14.2B Heusler alloy have been studied by direct measurements of the adiabatic temperature change (ΔTAD(T,H)) and indirectly by magnetization (M(T,H)), differential scanning calorimetry, and specific heat (C(T,H)) measurements. The presence of a first-order ferromagnetic-paramagnetic transition has been detected for Ni50Mn34.8In14.2B at 320 K. The magnetocaloric parameters, i.e., the magnetic entropy change (ΔSM = (2.9-3.2) J/kgK) and the adiabatic temperature change (ΔTAD = (1.3-1.52) K), have been evaluated for ΔH = 1.8 T from CP(T,H) and M(T,H) data and from direct ΔTAD(T,H) measurements. The extracted magnetocaloric parameters are comparable to those of Gd

INFLUENCE OF THE SURFACE STRUCTURE OF IMPLANTS ON THE CHARACTER OF THEIR INTERACTION WITH THE BONE TISSUE

The author considers the influence of microstructure of the surface of materials intended for implantation on the character of contact interaction with the bone tissue. The role of various kinds of surfaces of medical implants in efficiency of osseointegration processes and durability of fixation of implants in the bone tissue is defined. It is shown that the best conditions for osseointegration of implants are provided by the porous biocompatible coatings with heterogeneous morphology

BIOCOMPATIBLE METAL-OXIDE COATINGS WITH ANTISEPTIC PROPERTIES ON TRANSOSSEOUS IMPLANTS FOR TRAUMATOLOGY AND ORTHOPEDICS

Research in vivo was conducted in relation to the rod orthopedic implants with the biocompatible metal-oxide coverings modified with silver and copper – elements with antimicrobic activity. The author has demonstrated the basic possibility to effectively apply the metal-oxide coatings with antiseptic properties on titanium and steel implants for external transosseous osteosynthesis