Marko Obradović

Goodness-of-fit tests for Pareto distribution based on a characterization and their asymptotics

In this paper we present a new characterization of the Pareto distribution and consider goodness-of-fit tests based on it. We provide an integral and Kolmogorov–Smirnov-type statistics based on U-statistics and we calculate Bahadur efficiency for various alternatives. We find locally optimal alternatives for those tests. For small sample sizes, we compare the power of those tests with some common goodness-of-fit tests.

Three Characterizations of Exponential Distribution Involving Median of Sample of Size Three

In this paper three new characterizing theorems of exponential distribution are presented. They are based on equidistribution of some functions of order statistics. All of them include the median of sample of size three.

Selective Al-Ti reactivity in laser-processed Al/Ti multilayers

ABSTRACT Multilayers consisting of five (Al/Ti) bilayers were deposited on (100) silicon wafers. On top was deposited the Ti layer, aimed at preventing Al from diffusing to the surface upon laser treatment. The total thickness of the thin-film structure was 200 nm. Laser irradiations with Nd:YAG picoseconds laser pulses in the defocused regime were performed in air. Laser beam energy was 4 mJ and laser spot diameter on the sample surface was 3 mm (fluence 0.057 J cm−2). The samples were treated with different numbers of laser pulses. Structural characterizations were performed by different analytical methods and nano-hardness was also measured. Laser processing induced layer intermixing, formation of titanium aluminides, oxidation of the surface titanium layer and enhanced surface roughness. Aluminum appears at the sample surface only for the highest density of laser irradiation. Laser processing induces increment of nano-hardness by approximately 20% and decrease of residual Young’s modulus for a few percentages from the starting value of the untreated samples. These results can be interesting toward achieving structures with a selective extent of Al-Ti reactivity in this multilayered system, within the development of biocompatible materials.

Comparison of efficiencies of some symmetry tests around an unknown centre

ABSTRACT In this paper, some recent and classical tests of symmetry are modified for the case of an unknown centre. The unknown centre is estimated with its α-trimmed mean estimator. The asymptotic behaviour of the new tests is explored. The local approximate Bahadur efficiency is used to compare the tests to each other as well as to some other tests.

Study of pyrolysis of high density polyethylene in the open system and estimation of its capability for co-pyrolysis with lignite

Pyrolysis of high density polyethylene (HDPE) in the open system was studied. A plastic bag for food packing was used as a source of HDPE. Pyrolysis was performed at temperatures of 400, 450 and 500 °C, which were chosen based on thermogravimetric analysis. The HDPE pyrolysis yielded liquid, gaseous and solid products. Temperature rise resulted in the increase of conversion of HDPE into liquid and gaseous products. The main constituents of liquid pyrolysates are 1- n -alkenes, n -alkanes and terminal n -dienes. The composition of liquid products indicates that the performed pyrolysis of HDPE could not serve as a standalone operation for the production of gasoline or diesel, but preferably as a pre-treatment to yield a product to be blended into a refinery or petrochemical feed stream. The advantage of a liquid pyrolysate in comparison to crude oil is the extremely low content of aromatic hydrocarbons and the absence of polar compounds. The gaseous products have desirable composition and consist mainly of methane and ethene. The solid residues do not produce ash by combustion and have high calorific values. Co-pyrolysis of HDPE with mineral-rich lignite indicated positive synergetic effect at 450 and 500 °C, which is reflected through the increased experimental yields of liquid and gaseous products in comparison to theoretical ones.

Patterns of Abundance and Host Specificity of Bat Ectoparasites in the Central Balkans

Abstract Bats are hosts to a number of ectoparasites—acarines (ticks, chiggers, other mites), bat flies, and fleas. Bat ectoparasites might have significant ecological and public health importance as they may be potential vectors of zoonotic agents. It is important to identify their distribution, diversity, and host-parasite associations. Bat ectoparasites in the central Balkans have been largely understudied. The present research was conducted in 45 localities at the territory of Bosnia and Herzegovina, former Yugoslav Republic of Macedonia, Montenegro, and Serbia. In total, 1,143 individuals of 18 species of bats have been examined for the presence and abundance of ectoparasite species during 3 yr of research. In total, 21 ectoparasite species have been identified: three species of ticks, seven species of mites (including one species of chigger), eight species of bat flies, and three species of fleas. In total, 80 host-parasite associations have been identified. The largest number of ectoparasites parasitized primarily only one host species. The highest total number of hosts was identified for ectoparasite species Ixodes vespertilionis Koch, Nycteribia schmidlii Schiner, and Spinturnix myoti Kolenati. The spinturnicid mite Spinturnix psi Kolenati was the most abundant ectoparasite species and together with Penicilidia dufouri Westwood the most widely distributed species of bat ectoparasite, being present at 21 localities in the central Balkans. The presented data include the first systematic records of patterns of prevalence, mean intensity, mean abundance, and host specificity for bat ectoparasites in the central Balkans.

New Characterization-Based Symmetry Tests

Two new symmetry tests, of integral and Kolmogorov type, based on the characterization by squares of linear statistics are proposed. The test statistics are related to the family of degenerate U-statistics. Their asymptotic properties are explored. The maximal eigenvalue, needed for the derivation of their logarithmic tail behavior, was calculated or approximated using techniques from the theory of linear operators and the perturbation theory. The quality of the tests is assessed using the approximate Bahadur efficiency as well as the simulated powers. The tests are shown to be comparable with some recent and classical tests of symmetry.

Two-dimensional Kolmogorov-type goodness-of-fit tests based on characterisations and their asymptotic efficiencies

In this paper, new two-dimensional goodness-of-fit tests are proposed. They are of supremum type and are based on two different types of characterisations. The first type are those that involve functional equations that the distribution function satisfies, while the second type uses independence of some statistics. The asymptotics of the statistics is studied and Bahadur efficiencies of the tests against some close alternatives are calculated. In the process, a theorem on large deviations of Kolmogorov-type statistics has been extended to the multidimensional case.