Nagrinėjama silpnai priklausomų atsitiktinių dydžių statistika. Šio magistrinio darbo tikslas, turimą sumą, suvesti į nepriklausomų atsitiktinių dydžių sumą, kuri leistų tolimesniam tyrimui, pritaikyti žinomas teoremas, skaičiavimus bei rezultatus iš nepriklausomų atsitiktinių dydžių teorijos. / We analyze of weakly dependent random variables statistics. The objective of this master thesis is to deduce sum to independent random variables sum, which will be useful for applaying known theorems, calculations and results from the theory in independent random variables.

The automatic Algorithm ARI developed in this paper can generate variates from a large class of unimodal discrete distributions. It is only necessary to know the mode of the distribution and to have a subprogram available that can evaluate the probabilities. In a set up step the algorithm constructs a table mountain shaped hat function. Then rejection inversion, a new variant of the rejection method for discrete distributions that needs only one uniform random number per iteration, is used to sample from the desired distribution. It is shown that the expeceted number of iterations is uniformly bounded for all T-concave discrete distributions. Utilizing a simple squeeze or an auxiliary table of moderate size, which is initialized during generation and not in the set up, Algorithm ARI is fast, at least as fast as the fastest known methods designed for the Poisson, binomial and hypergeometric distributions. The set up time of the algorithm is not affected by the size of the domain of the distribution and is about ten times longer than the generation of one variate. Compared with the very fast and well known alias and indexed search methods the set up of Algorithm ARI is much faster but the generation time is about two times slower. More important than the speed is the fact that Algorithm ARI is the first automatic algorithm that can generate samples from discrete distributions with heavy tails. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

Financial market analysis nowadays constitutes an important pillar in central banks' monetary policy considerations. This is because the inherently forward-looking properties of asset prices can provide policy-makers with valuable information about future macroeconomic prospects, as seen through the eyes of investors. The five essays contained in this thesis elaborate upon three separate but complementary topics within the area of financial market research. First, the price discovery process of asset prices following releases of macroeconomic and monetary policy-related news is investigated. Such analysis can help in improving a central bank's understanding of how market participants update their views about future growth and inflation prospects. Second, an attempt is made to identify the factors which explain the time-varying co-movement of bond and stock prices. This analysis reveals that periods of negative correlation between the two assets tend to coincide with periods of very low investor risk appetite. Third, frequency distributions implied by options prices are often employed by central banks to assess the degree of uncertainty prevailing in markets as well as how the perceived balance of risks concerning future asset price movements is tilted. Various methods have been developed to estimate option-implied frequency distributions and the thesis assesses and compares the robustness of two of the most commonly used methods in central banks. / <p>Diss. Stockholm : Handelshögskolan, 2007 S. 9-16: sammanfattning, s. 17-160: 5 uppsatser</p>

In order to improve understanding of diesel soot oxidation, an experimental rig was designed and set up, in which the soot oxidation conditions, such as temperature, oxygen partial pressure, and CO2 partial pressure, could be varied independently of each other. The oxidizing gas flow in the oxidizer was under laminar condition. This test rig comprised a naturally-aspirated single cylinder engine which acted as the soot generator, and a separate premixed oxidation burner system in which soot extracted from the engine was oxidized under controlled conditions. Diesel soot was extracted from the engine exhaust pipe and from the engine pre-combustion chamber, and the soot-laden gas was then conveyed to the burner where it was oxidized. The burner was positioned vertically and it had a flat flame whose thickness was only a few millimetres. The hot gases from the flame flew upwards through a quartz transparent tube which acted as the soot oxidation duct. The soot-laden gas from the engine was premixed with the feedgas (itself a premixed mixture of methane, air, oxygen, and nitrogen) to the burner. The soot particles passed vertically through the flame front and continued burning in the post-flame gas flowing through the quartz tube oxidation duct. The oxygen concentration and temperature of the post-flame soot oxidation gas were controllable by adjusting the flowrate and composition of the burner feedgas. Diesel soot particles were sampled at different heights along the centreline of the quartz tube above the burner. Profiles of oxygen concentration, temperature, and soot particle velocity in the oxidation zone were thus measured. Morphology and size distributions of the sampled diesel soot particles were analyzed by means of Transmission Electron Microscopy (TEM) and a computer software called ImagePro Plus. Subsequently, the specific surface oxidation rates of the soot particles were worked out based on soot particle size distributions. The TEM micrographs obtained in this study showed that the diesel soot agglomerates existed in forms of clusters and chains, each containing between a small number and thousands of individual, mostly spherical tiny particles. Of order 97% of the individual spherical particles (spherules) had a size range from 10 to 80 nm. Occasionally, individual spherules of about 150 nm in diameter could be observed. The diesel soot particles sampled from the pre-chamber of the engine had different size distributions from those sampled from the exhaust of the engine, indicating that the soot underwent an oxidation process in the combustion chamber. Soot oxidation experiments were performed in the burner post-flame gas under oxygen partial pressures ranging from 0.010 to 0.050 atm and temperatures from 1520 to 1820 K. The test results showed that the oxidation rates of the diesel soot extracted from the diesel engine were generally lower than those predicted by the well-known Nagle and Strickland-Constable formula; however, the measured oxidation rates were higher than the predictions made with another well-known formula - the Lee formula. The soot extracted from the engine pre-chamber appeared not to oxidize as fast as the soot extracted from the exhaust of the engine. CO2 gas injection to the post-flame oxidation gas at constant oxygen partial pressure and oxidation temperature seemed to have accelerated the diesel soot oxidation rate. Based on the experimental results of this study and the results of other researchers, modifications to the Nagle and Strickland-Constable formula and to the Lee formula were accomplished. Also, an empirical expression, as an alternative to semi-empirical formulae, was worked out and presented in the thesis.

Different universal (also called automatic or black-box) methods have been suggested to sample from univariate log-concave distributions. The description of a universal generator for bivariate distributions has not been published up to now. The new algorithm for bivariate log-concave distributions is based on the method of transformed density rejection. In order to construct a hat function for a rejection algorithm the bivariate density is transformed by the logarithm into a concave function. Then it is possible to construct a dominating function by taking the minimum of several tangent planes which are by exponentiation transformed back into the original scale. The choice of the points of contact is automated using adaptive rejection sampling. This means that a point that is rejected by the rejection algorithm is used as additional point of contact until the maximal number of points of contact is reached. The paper describes the details how this main idea can be used to construct Algorithm ULC2D that can generate random pairs from bivariate log-concave distribution with a computable density. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

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We give an algorithm that can be used to sample from any discrete log-concave distribution (e.g. the binomial and hypergeometric distributions). It is based on rejection from a discrete dominating distribution that consists of parts of the geometric distribution. The algorithm is uniformly fast for all discrete log-concave distributions and not much slower than algorithms designed for a single distribution. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

The following thesis demonstrates two isotope tracing experiments that measure oxygen transport through electrochemically polarized solid oxides. Cathode-symmetric ‘button’ cells with yttria stabilized zirconia(YSZ) electrolytes and either strontium doped lanthanum manganate(LSM) or composite LSM/YSZ cathodes were studied. The first experiment measured the residence time distributions(RTD) of 34O2. The measured RTDs were compared at different temperatures(700-800°C) and applied potentials(-2 to -8V). Comparisons with simulated RTDs revealed that oxygen transport was laterally heterogeneous. Delamination of the counter electrode is likely the source of the heterogeneity. The second experiment measured a wave of 18O by exposing an interior cross section and applying ToF-SIMS analysis. A depth profile was produced that spans the cathode and electrolyte interface. The depth profile was compared with a variety of limiting oxygen activation scenarios predicted by a simple 1-D model. Comparisons demonstrated that oxygen activation is likely not restricted to the cathode and electrolyte interface.

The following thesis demonstrates two isotope tracing experiments that measure oxygen transport through electrochemically polarized solid oxides. Cathode-symmetric ‘button’ cells with yttria stabilized zirconia(YSZ) electrolytes and either strontium doped lanthanum manganate(LSM) or composite LSM/YSZ cathodes were studied. The first experiment measured the residence time distributions(RTD) of 34O2. The measured RTDs were compared at different temperatures(700-800°C) and applied potentials(-2 to -8V). Comparisons with simulated RTDs revealed that oxygen transport was laterally heterogeneous. Delamination of the counter electrode is likely the source of the heterogeneity. The second experiment measured a wave of 18O by exposing an interior cross section and applying ToF-SIMS analysis. A depth profile was produced that spans the cathode and electrolyte interface. The depth profile was compared with a variety of limiting oxygen activation scenarios predicted by a simple 1-D model. Comparisons demonstrated that oxygen activation is likely not restricted to the cathode and electrolyte interface.