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Tytuł:
On SαS density function
Autorzy:
Mazurkiewicz, Grażyna
Powiązania:
https://bibliotekanauki.pl/articles/729728.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
stable distribution
symmetric stable distribution
moments
scale mixture
Opis:
In this paper, we study some analytical properties of the symmetric α-stable density function.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2005, 25, 1; 91-101
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
USING THE STABLE DISTRIBUTION TO MONITOR A PROCESS, WHICH DISTRIBUTION IS UNKNOWN
Autorzy:
Chmielińska, Magdalena
Powiązania:
https://bibliotekanauki.pl/articles/655800.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
Control chart
stable distribution
Opis:
The control chart is a tool of statistical quality control, which is widely used in production. The fulfillment of its basic assumptions, guarantees flawless assessment of correctness of the monitored process. The purpose of this paper is to pay attention to the need to verify the assumptions of the used method and the effects of its unauthorized use, in case of not meeting its assumptions. In this paper a method that uses a family of stable distributions to estimate the unknown probability density of monitored diagnostic variable, is proposed. The estimated density function is the basis for determining the control limits.
Źródło:
Acta Universitatis Lodziensis. Folia Oeconomica; 2014, 3, 302
0208-6018
2353-7663
Pojawia się w:
Acta Universitatis Lodziensis. Folia Oeconomica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional lower order covariance based-estimator for Ornstein-Uhlenbeck process with stable distribution
Estymator bazujący na ułamkowych momentach dla procesu Ornsteina-Uhlenbecka z rozkładem stabilnym
Autorzy:
Kruczek, Piotr
Żuławiński, Wojciech
Pagacz, Patrycja
Wyłomańska, Agnieszka
Powiązania:
https://bibliotekanauki.pl/articles/953445.pdf
Data publikacji:
2019
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
ornstein-uhlenbeck process
floc
estimation
stable distribution
Opis:
The Ornstein-Uhlenbeck model is one of the most popular stochastic processes. It has found many interesting applications including physical phenomena. However, for many real data, the classical Ornstein-Uhlenbeck process cannot be applied. It is related to the fact that for many phenomena the vectors of observations exhibit so-called heavy-tailed behaviour. In such cases, the modifications of the classical models need to be used. In this paper, we analyze the Ornstein-Uhlenbeck process based on stable distribution. This distribution is one of the most classical members of the heavy-tailed class of distributions. In the literature, one can find various applications of stable processes. However, the heavy-tailed property implies that the classical methods of estimation and statistical investigation cannot be applied. In this paper, we propose a new method of estimation of stable Ornstein-Uhlenbeck process. This technique is based on the alternative measure of dependence, called fractional lower order covariance, which replaces the classical covariance for infinite-variance distribution. The proposed research is a continuation of the authors' previous studies, where the measure called covariation was proposed as the base for the estimation technique. We introduce the stable Ornstein-Uhlenbeck process and remind its main properties. In the main part, we define the new estimator of the of the parameters for discrete representation of Ornstein-Uhlenbeck process. Its effectiveness is checked by Monte Carlo simulations.
Źródło:
Mathematica Applicanda; 2019, 47, 2
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
GARCH(1,1) models with stable residuals
Autorzy:
Trusz, M.
Tserakh, U.
Powiązania:
https://bibliotekanauki.pl/articles/92862.pdf
Data publikacji:
2018
Wydawca:
Uniwersytet Przyrodniczo-Humanistyczny w Siedlcach
Tematy:
GARCH model
stable distributions
tempered stable distribution
maximum likelihood method
Opis:
The focus of this paper is the use of stable distributions for GARCH models. Such models are applied for the analysis of financial and economic time series, which have several special properties: volatility clustering, heavy tails and asymmetry of residuals distributions. Below we compare the properties of stable and tempered stable distributions and describe methodologies for constructing models and subsequent estimation of parameters using the maximum likelihood method. We also analyze an example of building models on real data in order to illustrate that tempered stable distributions could be used in financial time series models. Moreover, such distributions can show better results in comparison with traditionally used distributions.
Źródło:
Studia Informatica : systems and information technology; 2018, 1-2(22); 47-57
1731-2264
Pojawia się w:
Studia Informatica : systems and information technology
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of weighted myriad filters to suppress impulsive noise in biomedical signals
Autorzy:
Pander, T.
Powiązania:
https://bibliotekanauki.pl/articles/1965811.pdf
Data publikacji:
2004
Wydawca:
Politechnika Gdańska
Tematy:
weighted myriad filter
alpha-stable distribution
biomedical signals
Opis:
Biomedical signals are commonly recorded with many kinds of noise. One of these is a waveform of the electrical activity of muscles. This "natural" distortion is usually modelled with a white Gaussian noise. In order to suppress such noise a weighted myriad filter is applied. The weighted myriad filter belongs to a class of non-linear filters and requires knowledge about noise impulsiveness. An impulsive noise can be described with alpha-stable distributions. One objective of this paper is to apply alpha-stable distribution as a model of real-life muscle noise in ECG signals. The other objective of the paper is to apply a weighted myriad filter to suppress impulsive noise in biomedical (ECG) signals. The reference filters have been the Savitzky-Golay smoothing filter and the median filter. The obtained results have shown that alpha-stable distributions can be applied to model muscle noise and that a weighted myriad filter with a Chebyshev weighted function can effectively suppress such noise.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2004, 8, 2; 199-216
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Self-Adaptive Differential Evolution with Hybrid Rules of Perturbation for Dynamic Optimization
Autorzy:
Trojanowski, K.
Raciborski, M.
Kaczyński, P.
Powiązania:
https://bibliotekanauki.pl/articles/308439.pdf
Data publikacji:
2011
Wydawca:
Instytut Łączności - Państwowy Instytut Badawczy
Tematy:
adaptive differential evolution
dynamic optimization
symmetric a-stable distribution
Opis:
In this paper an adaptive differential evolution approach for dynamic optimization problems is studied. A new benchmark suite Syringa is also presented. The suite allows to generate test-cases from a multiple number of dynamic optimization classes. Two dynamic benchmarks: Generalized Dynamic Benchmark Generator (GDBG) and Moving Peaks Benchmark (MPB) have been simulated in Syringa and in the presented research they were subject of the experimental research. Two versions of adaptive differential evolution approach, namely the jDE algorithm have been heavily tested: the pure version of jDE and jDE equipped with solutions mutated with a new operator. The operator uses a symmetric ?-stable distribution variate for modification of the solution coordinates.
Źródło:
Journal of Telecommunications and Information Technology; 2011, 4; 20-30
1509-4553
1899-8852
Pojawia się w:
Journal of Telecommunications and Information Technology
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
k-th record estimator of the scale parameter of the α-stable distribution
Autorzy:
Stachura, Michał
Wodecka, Barbara
Powiązania:
https://bibliotekanauki.pl/articles/2156989.pdf
Data publikacji:
2022-12-15
Wydawca:
Główny Urząd Statystyczny
Tematy:
stable distribution
scale parameter estimator
k-th record values
Opis:
Various techniques of scale parameter estimation have been proposed in the case of alpha stable distributions. In the paper, the authors present an estimation technique that involves the k-th record theory. Although this theory is over 40 years old, its implementation in the classical extreme value theory – being the other cornerstone of the presented approach – is quite new, and tempting. Several theoretical properties of the introduced scale parameter estimators are presented. With the use of Monte Carlo methods, a comparative analysis is performed between the approach based on k-th records and approaches based on Hill’s and Pickands’ estimators. Additionally, the paper uses a real-life data set to illustrate how to effectively apply the k-th record estimator of the scale parameter. The research indicates several advantages of the k-th record approach over its other counterparts, especially when dealing with incomplete information about the underlying sample.
Źródło:
Statistics in Transition new series; 2022, 23, 4; 203-215
1234-7655
Pojawia się w:
Statistics in Transition new series
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stable distribution in application to fixational eye movement description
Autorzy:
Szmigiel, Marta
Grzesiek, Aleksandra
Wyłomańska, Agnieszka
Kasprzak, Henryk
Powiązania:
https://bibliotekanauki.pl/articles/174841.pdf
Data publikacji:
2019
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
eye movement
microsaccades
fixational eye movements
α-stable distribution
stochastic modelling
Opis:
To give an appropriate description of fixational eye movements is a very challenging problem. Over the years authors tried to describe the movements through different methods. The time series of the movements exhibit very characteristic behavior, which is the visible impulses. This may suggest the heavy-tailed distribution behind the data. In this paper on stochastic description of fixational eye movements, the α-stable distribution as the most important member of heavy-tailed family of distributions is proposed. The fixational eye movements together with head movement of both eyes of eight healthy subjects were measured and recorded by use of own designed optical system. Further analysis of changes in position of the pupil center in two-dimensional plane was performed. It was shown that head movement has very small impact on values of stability parameter α of fixational eye movements. The α-stable based analysis can be useful in better understanding of the character of the eye globe dynamics.
Źródło:
Optica Applicata; 2019, 49, 2; 365-377
0078-5466
1899-7015
Pojawia się w:
Optica Applicata
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Minimum dispersion coefficient criteria based positioning algorithm for BDS
Autorzy:
Wang, L.
Li, L.
Powiązania:
https://bibliotekanauki.pl/articles/141700.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
alpha-stable distribution
BeiDou satellites
Kalman filter
minimum dispersion coefficient criteria
non-Gaussian noise
positioning algorithm
Opis:
The BeiDou navigation satellite system (BDS) is one of the four global navigation satellite systems. More attention has been paid to the positioning algorithm of the BDS. Based on the study on the Kalman filter (KF) algorithm, this paper proposed a novel algorithm for the BDS, named as the minimum dispersion coefficient criteria Kalman filter (MDCCKF) positioning algorithm. The MDCCKF algorithm adopts minimum dispersion coefficient criteria (MDCC) to remove the influence of noise with an alpha-stable distribution (ASD) model which can describe non-Gaussian noise effectively, especially for the pulse noise in positioning. By minimizing the dispersion coefficient of the positioning error, the MDCCKF assures positioning accuracy under both Gaussian and non-Gaussian environment. Compared with the original KF algorithm, it is shown that the MDCCKF algorithm has higher positioning accuracy and robustness. The MDCCKF algorithm provides insightful results for potential future research.
Źródło:
Archives of Electrical Engineering; 2018, 67, 4; 739-753
1427-4221
2300-2506
Pojawia się w:
Archives of Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An Application of General Branching Processes to a Cell Cycle model With Two Uncoupled Subcycles and Unequal Cell Division
Autorzy:
Alexandersson, M.
Powiązania:
https://bibliotekanauki.pl/articles/929755.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
proces cykliczny komórki
matematyka
branching process
cell cycle model
unequal cell division
stable type distribution
alpha-curve
beta-curve
mother-daughter correlation
Opis:
A cell population model is constructed and analysed in the frameworkof general branching process theory. The model uses the idea that the DNA division cycle and the cell growth cycle are loosely coupled. The cell division is assumed to be unequal and the structure variables of the modelare size and growth, where the growth is regulated by supramitotic growth control. An explicit expression for the stable birth type distributionis given and asymptotics, such as the alpha- and beta_1-curve and various size distributions, are derived. We also prove that the microheterogeneity ingrowth causes the mother-daughter life length correlation to be non-negative.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2000, 10, 1; 131-145
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
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