Статті в журналах: "Non-stationary distribution"

1

Kislitsyn, Alexey Alexeevich, Antonina Borisovna Kozlova, Marina Borisovna Korsakova, Evgeniy Leonidovich Masherov, and Yurii Nikolaevich Orlov. "Stationary point of significance level for non-stationary distribution functions." Keldysh Institute Preprints, no. 113 (2018): 1–20. http://dx.doi.org/10.20948/prepr-2018-113.

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2

TARASOV, VASILY E. "CLASSICAL CANONICAL DISTRIBUTION FOR DISSIPATIVE SYSTEMS." Modern Physics Letters B 17, no. 23 (October 10, 2003): 1219–26. http://dx.doi.org/10.1142/s0217984903006268.

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We derive the canonical distribution as a stationary solution of the Liouville equation for the classical dissipative system. Dissipative classical systems can have stationary states that look like canonical Gibbs distributions. The condition for non-potential forces which leads to this stationary solution is very simple: the power of the non-potential forces must be directly proportional to the velocity of the Gibbs phase (phase entropy density) change. The example of the canonical distribution for a linear oscillator with friction is considered.

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3

Hesarkazzazi, Sina, Rezgar Arabzadeh, Mohsen Hajibabaei, Wolfgang Rauch, Thomas R. Kjeldsen, Ilaria Prosdocimi, Attilio Castellarin, and Robert Sitzenfrei. "Stationary vs non-stationary modelling of flood frequency distribution across northwest England." Hydrological Sciences Journal 66, no. 4 (March 12, 2021): 729–44. http://dx.doi.org/10.1080/02626667.2021.1884685.

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4

Foley, Robert D. "Stationary Poisson departure processes from non-stationary queues." Journal of Applied Probability 23, no. 1 (March 1986): 256–60. http://dx.doi.org/10.2307/3214138.

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We present some non-stationary infinite-server queueing systems with stationary Poisson departure processes. In Foley (1982), it was shown that the departure process from the Mt/Gt/∞ queue was a Poisson process, possibly non-stationary. The Mt/Gt/∞ queue is an infinite-server queue with a stationary or non-stationary Poisson arrival process and a general server in which the service time of a customer may depend upon the customer's arrival time. Mirasol (1963) pointed out that the departure process from the M/G/∞ queue is a stationary Poisson process. The question arose whether there are any other Mt/Gt/∞ queueing systems with stationary Poisson departure processes. For example, if the arrival rate is periodic, is it possible to select the service-time distribution functions to fluctuate in order to compensate for the fluctuations of the arrival rate? In this situation and in more general situations, it is possible to select the server such that the system yields a stationary Poisson departure process.

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5

Foley, Robert D. "Stationary Poisson departure processes from non-stationary queues." Journal of Applied Probability 23, no. 01 (March 1986): 256–60. http://dx.doi.org/10.1017/s0021900200106497.

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We present some non-stationary infinite-server queueing systems with stationary Poisson departure processes. In Foley (1982), it was shown that the departure process from the Mt/Gt/∞ queue was a Poisson process, possibly non-stationary. The Mt/Gt /∞ queue is an infinite-server queue with a stationary or non-stationary Poisson arrival process and a general server in which the service time of a customer may depend upon the customer's arrival time. Mirasol (1963) pointed out that the departure process from the M/G/∞ queue is a stationary Poisson process. The question arose whether there are any other Mt/Gt/∞ queueing systems with stationary Poisson departure processes. For example, if the arrival rate is periodic, is it possible to select the service-time distribution functions to fluctuate in order to compensate for the fluctuations of the arrival rate? In this situation and in more general situations, it is possible to select the server such that the system yields a stationary Poisson departure process.

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6

Behzadi, Mostafa, Mohd Bakri Adam, and Anwar Fitrianto. "Univariate Generalized Additive Models for Simulated Stationary and Non-Stationary Generalized Pareto Distribution." Journal of Mathematics and Statistics 13, no. 2 (February 1, 2017): 169–76. http://dx.doi.org/10.3844/jmssp.2017.169.176.

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7

Park, Namuk, and Songkuk Kim. "FlexSketch: Estimation of Probability Density for Stationary and Non-Stationary Data Streams." Sensors 21, no. 4 (February 4, 2021): 1080. http://dx.doi.org/10.3390/s21041080.

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Efficient and accurate estimation of the probability distribution of a data stream is an important problem in many sensor systems. It is especially challenging when the data stream is non-stationary, i.e., its probability distribution changes over time. Statistical models for non-stationary data streams demand agile adaptation for concept drift while tolerating temporal fluctuations. To this end, a statistical model needs to forget old data samples and to detect concept drift swiftly. In this paper, we propose FlexSketch, an online probability density estimation algorithm for data streams. Our algorithm uses an ensemble of histograms, each of which represents a different length of data history. FlexSketch updates each histogram for a new data sample and generates probability distribution by combining the ensemble of histograms while monitoring discrepancy between recent data and existing models periodically. When it detects concept drift, a new histogram is added to the ensemble and the oldest histogram is removed. This allows us to estimate the probability density function with high update speed and high accuracy using only limited memory. Experimental results demonstrate that our algorithm shows improved speed and accuracy compared to existing methods for both stationary and non-stationary data streams.

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8

Scala, Pietro, Giuseppe Cipolla, Dario Treppiedi, and Leonardo Valerio Noto. "The Use of GAMLSS Framework for a Non-Stationary Frequency Analysis of Annual Runoff Data over a Mediterranean Area." Water 14, no. 18 (September 13, 2022): 2848. http://dx.doi.org/10.3390/w14182848.

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Climate change affects all the components of the hydrological cycle. Starting from precipitation distribution, climate alterations have direct effects on both surface water and groundwater in terms of their quantity and quality. These effects lead to modifications in water availability for agriculture, ecology and other social uses. Change in rainfall patterns also affects the runoff of natural rivers. For this reason, studying runoff data according to classical hydrological approaches, i.e., statistical inference methods that exploit stationary probability distributions, might result in missing important information relevant to climate change. From this point of view, a new approach has to be found in the study of this type of data that allows for non-stationary analysis. In this study, the statistical framework known as Generalized Additive Models for Location, Scale and Shape (GAMLSS), which can be used to carry out non-stationary statistical analyses, was applied in a non-stationary frequency analysis of runoff data collected by four gauges widely distributed across Sicily (Italy) in the period 1916–1998. A classical stationary frequency analysis of these runoff data was followed by a different non-stationary frequency analysis; while the first was made using annual rainfall as a covariate, with the aim of understanding how certain statistical parameters of runoff distribution vary with changes in rainfall, the second derived information about the temporal variability of runoff frequencies by considering time as a covariate. A comparison between stationary and non-stationary approaches was carried out using the Akaike information criterion as a performance metric. After analyzing four different probability distributions, the non-stationary model with annual rainfall as a covariate was found to be the best among all those examined, and the three-parameter lognormal the most frequently preferred distribution.

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9

Crisci, Carolina, and Gonzalo Perera. "Asymptotic Extremal Distribution for Non-Stationary, Strongly-Dependent Data." Advances in Pure Mathematics 12, no. 08 (2022): 479–89. http://dx.doi.org/10.4236/apm.2022.128036.

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10

Ghosh, Ashish, and Heinz Muehlenbein. "Univariate marginal distribution algorithms for non-stationary optimization problems." International Journal of Knowledge-based and Intelligent Engineering Systems 8, no. 3 (January 10, 2005): 129–38. http://dx.doi.org/10.3233/kes-2004-8301.

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11

Hordijk, Arie, and AD Ridder. "Insensitive bounds for the stationary distribution of non-reversible Markov chains." Journal of Applied Probability 25, no. 1 (March 1988): 9–20. http://dx.doi.org/10.2307/3214229.

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A general method is developed to compute easy bounds of the weighted stationary probabilities for networks of queues which do not satisfy the standard product form. The bounds are obtained by constructing approximating reversible Markov chains. Thus, the bounds are insensitive with respect to service-time distributions. A special representation, called the tree-form solution, of the stationary distribution is used to derive the bounds. The results are applied to an overflow model.

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12

Hordijk, Arie, and AD Ridder. "Insensitive bounds for the stationary distribution of non-reversible Markov chains." Journal of Applied Probability 25, no. 01 (March 1988): 9–20. http://dx.doi.org/10.1017/s0021900200040596.

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A general method is developed to compute easy bounds of the weighted stationary probabilities for networks of queues which do not satisfy the standard product form. The bounds are obtained by constructing approximating reversible Markov chains. Thus, the bounds are insensitive with respect to service-time distributions. A special representation, called the tree-form solution, of the stationary distribution is used to derive the bounds. The results are applied to an overflow model.

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13

Chen, Weirong, Jiaqi Zheng, Haoyu Yu, Guihai Chen, Yixin Chen, and Dongsheng Li. "Online Learning Bipartite Matching with Non-stationary Distributions." ACM Transactions on Knowledge Discovery from Data 16, no. 5 (October 31, 2022): 1–22. http://dx.doi.org/10.1145/3502734.

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Online bipartite matching has attracted wide interest since it can successfully model the popular online car-hailing problem and sharing economy. Existing works consider this problem under either adversary setting or i.i.d. setting. The former is too pessimistic to improve the performance in the general case; the latter is too optimistic to deal with the varying distribution of vertices. In this article, we initiate the study of the non-stationary online bipartite matching problem, which allows the distribution of vertices to vary with time and is more practical. We divide the non-stationary online bipartite matching problem into two subproblems, the matching problem and the selecting problem, and solve them individually. Combining Batch algorithms and deep Q-learning networks, we first construct a candidate algorithm set to solve the matching problem. For the selecting problem, we use a classical online learning algorithm, Exp3, as a selector algorithm and derive a theoretical bound. We further propose CDUCB as a selector algorithm by integrating distribution change detection into UCB. Rigorous theoretical analysis demonstrates that the performance of our proposed algorithms is no worse than that of any candidate algorithms in terms of competitive ratio. Finally, extensive experiments show that our proposed algorithms have much higher performance for the non-stationary online bipartite matching problem comparing to the state-of-the-art.

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14

Vu, Thi Thu Nga, Gilbert Teyssedre, and Séverine Le Roy. "Electric Field Distribution in HVDC Cable Joint in Non-Stationary Conditions." Energies 14, no. 17 (August 30, 2021): 5401. http://dx.doi.org/10.3390/en14175401.

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Accessories such as joints and terminations represent weak points in HVDC cable systems. The DC field distribution is intimately dependent on the thermal conditions of the accessory and on material properties. Moreover, there is no available method to probe charge distribution in these conditions. In this work, the field distribution in non-stationary conditions, both thermally and electrically, is computed considering crosslinked polyethylene (XLPE) as cable insulation and different insulating materials (silicone, rubber, XLPE) for a 200 kV joint assembled in a same geometry. In the conditions used, i.e., temperatures up to 70 °C, and with the material properties considered, the dielectric time constant appears of the same order or longer than the thermal one and is of several hours. This indicates that both physical phenomena need to be considered for modelling the electric field distribution. Both the radial and the tangential field distributions are analysed, and focus is given on the field distribution under the stress cone on the ground side and near the central deflector on the high voltage side of the joint. We show that the position of the maximum field varies in time in a way that is not easy to anticipate. Under the cone, the smallest tangential field is obtained with the joint insulating material having the highest electrical conductivity. This results from a shift of the field towards the cable insulation in which the geometrical features produce a weaker axial component of the field. At the level of the central deflector, it is clear that the tangential field is higher when the mismatch between the conductivity of the two insulations is larger. In addition, the field grows as a function of time under stress. This work shows the need of precise data on materials conductivity and the need of probing field distribution in 3D.

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15

Mahnke, Reinhard, Jevgenijs Kaupužs, and Mārtiņš Brics. "Power Laws and Skew Distributions." Communications in Computational Physics 12, no. 3 (September 2012): 721–31. http://dx.doi.org/10.4208/cicp.010411.050811a.

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AbstractPower-law distributions and other skew distributions, observed in various models and real systems, are considered. A model, describing evolving systems with increasing number of elements, is considered to study the distribution over element sizes. Stationary power-law distributions are found. Certain non-stationary skew distributions are obtained and analyzed, based on exact solutions and numerical simulations.

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16

Jung, Byungsoon, Taewoong Kang, and Junyong Ahn. "Calculation of Storm Surge by Non-stationary GEV Distribution Model." Journal of the Korean Society of Hazard Mitigation 18, no. 5 (August 31, 2018): 285–92. http://dx.doi.org/10.9798/kosham.2018.18.5.285.

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17

Ciannelli, Lorenzo, Valerio Bartolino, and Kung-Sik Chan. "Non-additive and non-stationary properties in the spatial distribution of a large marine fish population." Proceedings of the Royal Society B: Biological Sciences 279, no. 1743 (June 20, 2012): 3635–42. http://dx.doi.org/10.1098/rspb.2012.0849.

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Density-independent and density-dependent variables both affect the spatial distributions of species. However, their effects are often separately addressed using different analytical techniques. We apply a spatially explicit regression framework that incorporates localized, interactive and threshold effects of both density-independent (water temperature) and density-dependent (population abundance) variables, to study the spatial distribution of a well-monitored flatfish population in the eastern Bering Sea. Results indicate that when population biomass was beyond a threshold a further increase in biomass-promoted habitat expansion in a non-additive fashion with water temperature. In contrast, during years of low population size, habitat occupancy was affected positively only by water temperature. These results reveal the spatial signature of intraspecific abundance distribution relationships as well as the non-additive and non-stationary responses of species spatial dynamics. Furthermore, these results underscore the importance of implementing analytical techniques that can simultaneously account for density-dependent and density-independent sources of variability when studying geographical distribution patterns.

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18

Wang, Peng, Ji Hua Cao, and Xiao Chang Ni. "Blind Separation of Non-Stationary Convoluted Mixtures Based on Time-Frequency Analysis." Advanced Materials Research 538-541 (June 2012): 2571–75. http://dx.doi.org/10.4028/www.scientific.net/amr.538-541.2571.

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The signals of convoluted mixtures have a stated of non-stationary identity, and the change of their spectrum with time-varying usually could not be observed from the frequency domain, but they can be observed by the time-frequency method. Therefore, the blind separation of non-stationary convoluted mixtures based on time-frequency analysis is proposed in this paper. For the non-stationary identity, the space-albinism of the mixed matrices and the joint diagonalization of the time-frequency matrices are simulated to separate the convoluted mixtures. Two kinds of time-frequency analysis methods, Wigner-Ville distribution and improved Wigner-Ville distribution, are introduced, which are calculated with MATLAB 7.0 software. The simulated results show the improved Wigner-Ville distribution method has a better performance for blind separating of non-stationary convoluted and mixed signals.

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19

Nogaj, M., S. Parey, and D. Dacunha-Castelle. "Non-stationary extreme models and a climatic application." Nonlinear Processes in Geophysics 14, no. 3 (June 25, 2007): 305–16. http://dx.doi.org/10.5194/npg-14-305-2007.

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Abstract. In this paper, we study extreme values of non-stationary climatic phenomena. In the usually considered stationary case, the modelling of extremes is only based on the behaviour of the tails of the distribution of the remainder of the data set. In the non-stationary case though, it seems reasonable to assume that the temporal dynamics of the entire data set and that of extremes are closely related and thus all the available information about this link should be used in statistical studies of these events. We try to study how centered and normalized data which are closer to stationary data than the observation allows easier statistical analysis and to understand if we are very far from a hypothesis stating that the extreme events of centered and normed data follow a stationary distribution. The location and scale parameters used for this transformation (the central field), as well as extreme parameters obtained for the transformed data enable us to retrieve the trends in extreme events of the initial data set. Through non-parametric statistical methods, we thus compare a model directly built on the extreme events and a model reconstructed from estimations of the trends of the location and scale parameters of the entire data set and stationary extremes obtained from the centered and normed data set. In case of a correct reconstruction, we can clearly state that variations of the characteristics of extremes are well explained by the central field. Through these analyses we bring arguments to choose constant shape parameters of extreme distributions. We show that for the frequency of the moments of high threshold excesses (or for the mean of annual extremes), the general dynamics explains a large part of the trends on frequency of extreme events. The conclusion is less obvious for the amplitudes of threshold exceedances (or the variance of annual extremes) – especially for cold temperatures, partly justified by the statistical tools used, which require further analyses on the variability definition.

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20

Gruss, Łukasz, Mirosław Wiatkowski, Paweł Tomczyk, Jaroslav Pollert, and Jaroslav Pollert. "Comparison of Three-Parameter Distributions in Controlled Catchments for a Stationary and Non-Stationary Data Series." Water 14, no. 3 (January 19, 2022): 293. http://dx.doi.org/10.3390/w14030293.

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Flood Frequency Analysis (FFA) and the non-stationary FFA approaches are used in flood study, water resource planning, and the design of hydraulic structures. However, there is still a need to develop these methods and to find new procedures that can be used in estimating simple distributions in controlled catchments. The aim of the study is a comparison of three-parameter distributions in controlled catchments for stationary and non-stationary data series and further to develop the procedure of the estimation the simple distributions. Ten rivers from the Czech Republic and Poland were selected because of their existing or planned reservoirs as well as for flood protection reasons. The annual maximum method and the three-parameter Weibull, Log-Normal, Generalized extreme value, and Pearson Type III distributions were used in this study. The analyzed time series are stationary and non-stationary. The methodology used in this study, which makes use of the Maximum Likelihood Estimation, allows one to simplify the analysis whenever there is a series of data that is both stationary and non-stationary. The novelty in our research is the standardization and development of a new procedure for a stationary and non-stationary data series, taking into account to read a specific value of the maximum flow with a given exceedance probability from the lower or upper tail. It determines the optimal choice of the theoretical distribution that can be used, for example in the design of weirs in rural areas (lower quantiles) or in the design of hydrotechnical structures in areas at risk of flooding (upper quantiles).

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21

Pleshakov, Ruslan V. "Simulation of non-stationary event flow with a nested stationary component." Discrete and Continuous Models and Applied Computational Science 28, no. 1 (December 15, 2020): 35–48. http://dx.doi.org/10.22363/2658-4670-2020-28-1-35-48.

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A method for constructing an ensemble of time series trajectories with a nonstationary flow of events and a non-stationary empirical distribution of the values of the observed random variable is described. We consider a special model that is similar in properties to some real processes, such as changes in the price of a financial instrument on the exchange. It is assumed that a random process is represented as an attachment of two processes - stationary and non-stationary. That is, the length of a series of elements in the sequence of the most likely event (the most likely price change in the sequence of transactions) forms a non-stationary time series, and the length of a series of other events is a stationary random process. It is considered that the flow of events is non-stationary Poisson process. A software package that solves the problem of modeling an ensemble of trajectories of an observed random variable is described. Both the values of a random variable and the time of occurrence of the event are modeled. An example of practical application of the model is given.

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22

Pleshakov, Ruslan V. "Simulation of non-stationary event flow with a nested stationary component." Russian Family Doctor 28, no. 1 (December 15, 2020): 35–48. http://dx.doi.org/10.17816/rfd10640.

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A method for constructing an ensemble of time series trajectories with a nonstationary flow of events and a non-stationary empirical distribution of the values of the observed random variable is described. We consider a special model that is similar in properties to some real processes, such as changes in the price of a financial instrument on the exchange. It is assumed that a random process is represented as an attachment of two processes - stationary and non-stationary. That is, the length of a series of elements in the sequence of the most likely event (the most likely price change in the sequence of transactions) forms a non-stationary time series, and the length of a series of other events is a stationary random process. It is considered that the flow of events is non-stationary Poisson process. A software package that solves the problem of modeling an ensemble of trajectories of an observed random variable is described. Both the values of a random variable and the time of occurrence of the event are modeled. An example of practical application of the model is given.

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23

Pleshakov, Ruslan V. "Simulation of non-stationary event flow with a nested stationary component." Russian Family Doctor 28, no. 1 (December 15, 2020): 35–48. http://dx.doi.org/10.17816/rfd10645.

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A method for constructing an ensemble of time series trajectories with a nonstationary flow of events and a non-stationary empirical distribution of the values of the observed random variable is described. We consider a special model that is similar in properties to some real processes, such as changes in the price of a financial instrument on the exchange. It is assumed that a random process is represented as an attachment of two processes - stationary and non-stationary. That is, the length of a series of elements in the sequence of the most likely event (the most likely price change in the sequence of transactions) forms a non-stationary time series, and the length of a series of other events is a stationary random process. It is considered that the flow of events is non-stationary Poisson process. A software package that solves the problem of modeling an ensemble of trajectories of an observed random variable is described. Both the values of a random variable and the time of occurrence of the event are modeled. An example of practical application of the model is given.

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24

Chen, Xiaohong, Changqing Ye, Jiaming Zhang, Chongyu Xu, Lijuan Zhang, and Yihan Tang. "Selection of an Optimal Distribution Curve for Non-Stationary Flood Series." Atmosphere 10, no. 1 (January 15, 2019): 31. http://dx.doi.org/10.3390/atmos10010031.

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The stationarity assumption of hydrological processes has long been compromised by human disturbances in river basins. The traditional hydrological extreme-value analysis method, i.e., “extreme value theory” which assumes stationarity of the time series, needs to be amended in order to adapt to these changes. In this paper, taking the East River basin, south China as a case study, a framework was put forward for selection of a suitable distribution curve for non-stationary flood series by using the time-varying moments (TVM). Data used for this study are the annual maximum daily flow of 1954–2009 at the Longchuan, Heyuan and Boluo Stations in the study basin. Five types of distribution curves and eight kinds of trend models, for a combination of 40 models, were evaluated and compared. The results showed that the flood series and optimal distribution curves in the East River basin have been significantly impacted by a continuously changing environment. With the increase of the degree of human influence, the thinner tails of distributions are more suitable for fitting the observed flow data, and the trend models are changed from CP (mean and standard deviation fitted by parabolic trend model) to CL (mean and standard deviation fitted by linear trend model) from upstream to downstream of the catchment. The design flood flow corresponding to a return period of more than 10 years at the Longchuan, Heyuan and Boluo Stations was overestimated by more than 28.36%, 53.24% and 26.06%, respectively if the non-stationarity of series is not considered and the traditional method is still used for calculation. The study reveals that in a changing environment, more advanced statistical methods that explicitly account for the non-stationarity of extreme flood characteristics are required.

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25

Campos-Aranda, Daniel Francisco. "Ajuste de la distribución no estacionaria GVE11 a través de momentos L." Tecnología y ciencias del agua 12, no. 3 (May 1, 2021): 164–203. http://dx.doi.org/10.24850/j-tyca-2021-03-05.

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26

Bergamelli, Michele, Jan Novotný, and Giovanni Urga. "Maximum Non-Extensive Entropy Block Bootstrap for Non-stationary Processes." Articles 91, no. 1-2 (May 20, 2016): 115–39. http://dx.doi.org/10.7202/1036916ar.

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In this paper, we propose a novel entropy-based resampling scheme valid for non-stationary data. In particular, we identify the reason for the failure of the original entropy-based algorithm of Vinod and López-de Lacalle (2009) to be the perfect rank correlation between the actual and bootstrapped time series. We propose the Maximum Entropy Block Bootstrap which preserves the rank correlation locally. Further, we also introduce the Maximum non-extensive Entropy Block Bootstrap to allow for fat tail behaviour in time series. Finally, we show the optimal finite sample properties of the proposed methods via a Monte Carlo analysis where we bootstrap the distribution of the Dickey-Fuller test.

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27

Rudenko, Oleg, and Oleksandr Bezsonov. "Adaptive identification under the maximum correntropy criterion with variable center." RADIOELECTRONIC AND COMPUTER SYSTEMS, no. 1 (February 23, 2022): 216–28. http://dx.doi.org/10.32620/reks.2022.1.17.

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The problem of identifying the parameters of a linear object in the presence of non-Gaussian noise is considered. The identification algorithm is a gradient procedure for maximizing the functional, which is a correntropy. This functionality allows you to get estimates that have robust properties. In contrast to the commonly used Gaussian kernels, the centers of which are at zero and effective for distributions with zero mean, the paper considers a modification of the criterion suitable for distributions with nonzero mean. The modification is to use correntropy with a variable center The use of Gaussian kernels with a variable center will allow us to estimate unknown parameters under Gaussian and non-Gaussian noises with zero and non-zero mean distributions and provide an opportunity to develop new technologies for data analysis and processing. It is important to develop a robust identification algorithm based on correntropy with variable center. Their properties in the identification of stationary and non-stationary objects are the subject of research. The goal is to develop a robust identification algorithm that maximizes the criterion of correntropy with a variable center using center configuration procedures and kernel width and to study its convergence in stationary and non-stationary cases under non-Gaussian noise. Expressions for steady-state value of the estimation error are obtained, which depend on the type of noise distribution and the degree of non-stationarity of the estimated parameters The following tasks are solved: to investigate the convergence of the algorithm and determine the conditions for the stability of the established identification process. Methods of estimation theory (identification) and probability theory are used. The following results were obtained: 1) the developed algorithm provides robust estimates in the presence of noises having a distribution with zero and non-zero mean; 2) its convergence was studied in stationary and non-stationary cases under conditions of Gaussian and non-Gaussian noise; 3) simulation of the algorithm was carried out. 1) the developed algorithm consists in the development of a robust identification algorithm that maximizes the criterion of correntropy with a variable center; 2) its convergence in stationary and non-stationary cases in the conditions of Gaussian and non-Gaussian noises is investigated; 3) simulation of the algorithm is performed. Conclusions: The results of the current study will improve existing data processing technologies based on robust estimates and accelerate the development of new computing programs in real time.

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28

Artemov, V., L. Artemova, V. Korotaev, and A. Kuznetsov. "RESULTS OF “BENCHMARK ROSTOV 2” TEST TASK SIMULATION USING SAPFIR_95&RC_VVER AND KORSAR PROGRAM PACKAGE." PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. SERIES: NUCLEAR AND REACTOR CONSTANTS 2019, no. 4 (December 26, 2019): 118–27. http://dx.doi.org/10.55176/2414-1038-2019-4-118-127.

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This paper presents the results of “Benchmark Rostov 2” test task simulation using SAPFIR_95&RC_VVER program package; the test task is based on a full-scale experiment performed at the Rostov NPP, where the transition mode with boric acid dilution and a working group insertion to compensate the reactivity were implemented. The purpose of this task is to develop the methods of non-stationary computation of pin-by-pin power energy distribution in calculation programs for neutronic and thermohydraulic characteristics of VVER-type reactors. The SAPFIR_95&RC_VVER program package uses two calculation methods of pin-by-pin power energy distribution: micro- and macro-flux superposition method and combined fine-grid method, where the nodes of radial computational grid in the reactor core coincide with the centers of fuel elements in fuel rod assembly. The combined fine-grid method for calculating pin-by-pin power energy distribution is carried out with the known values of burn-up distributions, fuel temperature, and coolant density obtained from superposition method. Both approaches are used for solving stationary and non-stationary tasks. When simulating the non-stationary processes, the test task can be solved in conjunction with KORSAR thermohydraulic code. This paper describes neutronic models of VVER-1000 reactor core used in “Benchmark Rostov 2” test task for superposition method and combined method. Calculation results for power energy distribution fields are given.

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29

Lu, Shiyin, Yao Hu, and Lijun Zhang. "Stochastic Bandits with Graph Feedback in Non-Stationary Environments." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 10 (May 18, 2021): 8758–66. http://dx.doi.org/10.1609/aaai.v35i10.17061.

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We study a variant of stochastic bandits where the feedback model is specified by a graph. In this setting, after playing an arm, one can observe rewards of not only the played arm but also other arms that are adjacent to the played arm in the graph. Most of the existing work assumes the reward distributions are stationary over time, which, however, is often violated in common scenarios such as recommendation systems and online advertising. To address this limitation, we study stochastic bandits with graph feedback in non-stationary environments and propose algorithms with graph-dependent dynamic regret bounds. When the number of reward distribution changes L is known in advance, one of our algorithms achieves an Õ(√(αLT)) dynamic regret bound. We also develop an adaptive algorithm that can adapt to unknown L and attain an Õ(√(θLT)) dynamic regret. Here, α and θ are some graph-dependent quantities and T is the time horizon.

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30

Haoyu, Zhao, and Chen Wei. "Online Second Price Auction with Semi-Bandit Feedback under the Non-Stationary Setting." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 6893–900. http://dx.doi.org/10.1609/aaai.v34i04.6171.

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In this paper, we study the non-stationary online second price auction problem. We assume that the seller is selling the same type of items in T rounds by the second price auction, and she can set the reserve price in each round. In each round, the bidders draw their private values from a joint distribution unknown to the seller. Then, the seller announced the reserve price in this round. Next, bidders with private values higher than the announced reserve price in that round will report their values to the seller as their bids. The bidder with the highest bid larger than the reserved price would win the item and she will pay to the seller the price equal to the second-highest bid or the reserve price, whichever is larger. The seller wants to maximize her total revenue during the time horizon T while learning the distribution of private values over time. The problem is more challenging than the standard online learning scenario since the private value distribution is non-stationary, meaning that the distribution of bidders' private values may change over time, and we need to use the non-stationary regret to measure the performance of our algorithm. To our knowledge, this paper is the first to study the repeated auction in the non-stationary setting theoretically. Our algorithm achieves the non-stationary regret upper bound Õ(min{√S T, V¯⅓T⅔), where S is the number of switches in the distribution, and V¯ is the sum of total variation, and S and V¯ are not needed to be known by the algorithm. We also prove regret lower bounds Ω(√S T) in the switching case and Ω(V¯⅓T⅔) in the dynamic case, showing that our algorithm has nearly optimal non-stationary regret.

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31

Inuzuka, Hiroshi, Takayoshi Nagai, and Takashige Tsukishima. "Analysis of non-stationary plasma experimental data by the Wigner distribution." Kakuyūgō kenkyū 60, no. 3 (1988): 217–28. http://dx.doi.org/10.1585/jspf1958.60.217.

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32

Chihi, H., and G. De Marsily. "Simulating Non-Stationary Seismic Facies Distribution in a Prograding Shelf Environment." Oil & Gas Science and Technology - Revue de l'IFP 64, no. 4 (July 2009): 451–67. http://dx.doi.org/10.2516/ogst/2009017.

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33

KAWAKAMI, Takashi, Nobuyuki YASUI, Hajime KITAGAWA, Satoshi HORIHATA, and Syunsuke ISHIMITSU. "Reconstruction of Non stationary Signals by Inverse Transform of Wigner Distribution." Transactions of the Japan Society of Mechanical Engineers Series C 63, no. 607 (1997): 975–81. http://dx.doi.org/10.1299/kikaic.63.975.

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34

Hierro, María, and Adolfo Maza. "Non-stationary transition matrices: An overlooked issue in intra-distribution dynamics." Economics Letters 103, no. 2 (May 2009): 107–9. http://dx.doi.org/10.1016/j.econlet.2009.02.005.

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35

Astola, Jaakko, and Eduard Danielian. "On regularly varying distributions generated by birth-death process." Facta universitatis - series: Electronics and Energetics 19, no. 1 (2006): 109–31. http://dx.doi.org/10.2298/fuee0601109a.

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Skewed distributions generated by birth-death process with different particular forms of intensivities? moderate growth are used in biomolecular systems and various non-mathematical fields. Based on datasets of biomolecular systems such distributions have to exhibit the power law like behavior at infinity, i.e. regular variation. In the present paper for the standard birth-death process with most general than before assumptions on moderate growth of intensivities the following problems are solved. 1. The stationary distribution varies regularly if the sequence of intensivities varies regularly. 2. The slowly varying component and the exponent of regular variation of stationary distribution are found.

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36

Shinohara, Shuji, Nobuhito Manome, Yoshihiro Nakajima, Yukio Pegio Gunji, Toru Moriyama, Hiroshi Okamoto, Shunji Mitsuyoshi, and Ung-il Chung. "Power Laws Derived from a Bayesian Decision-Making Model in Non-Stationary Environments." Symmetry 13, no. 4 (April 19, 2021): 718. http://dx.doi.org/10.3390/sym13040718.

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The frequency of occurrence of step length in the migratory behaviour of various organisms, including humans, is characterized by the power law distribution. This pattern of behaviour is known as the Lévy walk, and the reason for this phenomenon has been investigated extensively. Especially in humans, one possibility might be that this pattern reflects the change in self-confidence in one’s chosen behaviour. We used simulations to demonstrate that active assumptions cause changes in the confidence level in one’s choice under a situation of lack of information. More specifically, we presented an algorithm that introduced the effects of learning and forgetting into Bayesian inference, and simulated an imitation game in which two decision-making agents incorporating the algorithm estimated each other’s internal models. For forgetting without learning, each agents’ confidence levels in their own estimation remained low owing to a lack of information about the counterpart, and the agents changed their hypotheses about the opponent frequently, and the frequency distribution of the duration of the hypotheses followed an exponential distribution for a wide range of forgetting rates. Conversely, when learning was introduced, high confidence levels occasionally occurred even at high forgetting rates, and exponential distributions universally turned into power law distribution.

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37

Cavaliere, Giuseppe, Iliyan Georgiev, and A. M. Robert Taylor. "UNIT ROOT INFERENCE FOR NON-STATIONARY LINEAR PROCESSES DRIVEN BY INFINITE VARIANCE INNOVATIONS." Econometric Theory 34, no. 2 (May 3, 2016): 302–48. http://dx.doi.org/10.1017/s0266466616000037.

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The contribution of this paper is two-fold. First, we derive the asymptotic null distribution of the familiar augmented Dickey-Fuller [ADF] statistics in the case where the shocks follow a linear process driven by infinite variance innovations. We show that these distributions are free of serial correlation nuisance parameters but depend on the tail index of the infinite variance process. These distributions are shown to coincide with the corresponding results for the case where the shocks follow a finite autoregression, provided the lag length in the ADF regression satisfies the same o(T1/3) rate condition as is required in the finite variance case. In addition, we establish the rates of consistency and (where they exist) the asymptotic distributions of the ordinary least squares sieve estimates from the ADF regression. Given the dependence of their null distributions on the unknown tail index, our second contribution is to explore sieve wild bootstrap implementations of the ADF tests. Under the assumption of symmetry, we demonstrate the asymptotic validity (bootstrap consistency) of the wild bootstrap ADF tests. This is done by establishing that (conditional on the data) the wild bootstrap ADF statistics attain the same limiting distribution as that of the original ADF statistics taken conditional on the magnitude of the innovations.

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38

Shimizu, Keita, Tadashi Yamada, and Tomohito J. Yamada. "Introduction of Confidence Interval Based on Probability Limit Method Test into Non-Stationary Hydrological Frequency Analysis." Water 12, no. 10 (September 29, 2020): 2727. http://dx.doi.org/10.3390/w12102727.

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Nonstationarity in hydrological variables has been identified throughout Japan in recent years. As a result, the reliability of designs derived from using method based on the assumption of stationary might deteriorate. Non-stationary hydrological frequency analysis is among the measures to counter this possibility. Using this method, time variations in the probable hydrological quantity can be estimated using a non-stationary extreme value distribution model with time as an explanatory variable. In this study, we build a new method for constructing the confidence interval regarding the non-stationary extreme value distribution by applying a theory of probability limit method test. Furthermore, by introducing a confidence interval based on probability limit method test into the non-stationary hydrological frequency analysis, uncertainty in design rainfall because of lack of observation information was quantified, and it is shown that assessment pertaining to both the occurrence risk of extremely heavy rainfall and changes in the trend of extreme rainfall accompanied with climate change is possible.

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39

Mentaschi, Lorenzo, Michalis Vousdoukas, Evangelos Voukouvalas, Ludovica Sartini, Luc Feyen, Giovanni Besio, and Lorenzo Alfieri. "The transformed-stationary approach: a generic and simplified methodology for non-stationary extreme value analysis." Hydrology and Earth System Sciences 20, no. 9 (September 5, 2016): 3527–47. http://dx.doi.org/10.5194/hess-20-3527-2016.

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Abstract. Statistical approaches to study extreme events require, by definition, long time series of data. In many scientific disciplines, these series are often subject to variations at different temporal scales that affect the frequency and intensity of their extremes. Therefore, the assumption of stationarity is violated and alternative methods to conventional stationary extreme value analysis (EVA) must be adopted. Using the example of environmental variables subject to climate change, in this study we introduce the transformed-stationary (TS) methodology for non-stationary EVA. This approach consists of (i) transforming a non-stationary time series into a stationary one, to which the stationary EVA theory can be applied, and (ii) reverse transforming the result into a non-stationary extreme value distribution. As a transformation, we propose and discuss a simple time-varying normalization of the signal and show that it enables a comprehensive formulation of non-stationary generalized extreme value (GEV) and generalized Pareto distribution (GPD) models with a constant shape parameter. A validation of the methodology is carried out on time series of significant wave height, residual water level, and river discharge, which show varying degrees of long-term and seasonal variability. The results from the proposed approach are comparable with the results from (a) a stationary EVA on quasi-stationary slices of non-stationary series and (b) the established method for non-stationary EVA. However, the proposed technique comes with advantages in both cases. For example, in contrast to (a), the proposed technique uses the whole time horizon of the series for the estimation of the extremes, allowing for a more accurate estimation of large return levels. Furthermore, with respect to (b), it decouples the detection of non-stationary patterns from the fitting of the extreme value distribution. As a result, the steps of the analysis are simplified and intermediate diagnostics are possible. In particular, the transformation can be carried out by means of simple statistical techniques such as low-pass filters based on the running mean and the standard deviation, and the fitting procedure is a stationary one with a few degrees of freedom and is easy to implement and control. An open-source MATLAB toolbox has been developed to cover this methodology, which is available at https://github.com/menta78/tsEva/ (Mentaschi et al., 2016).

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40

Gutsul, I. V., and V. I. Gutsul. "Peculiarities of Non-Stationary Temperature Distribution of Optical Non-Transparent Anisotropic Thermoelement at Impulse Ray Excitement." Фізика і хімія твердого тіла 16, no. 2 (June 30, 2015): 261–65. http://dx.doi.org/10.15330/pcss.16.2.261-2165.

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The solutions of the non-stationary equation of thermoconductivity for the optical non-transparent thermoelement at impulse ray excitement are presented in the paper for two-time ranges: when the ray current falls (0<t<tau) and when it stops (t<tau). It is shown that the behavior of temperature distributions essentially depends on the relationship between the impulse duration (tau) and relaxation time (tau0) of temperature shifts over the whole volume of anisotropic thermoelement, arising at the impulse ray excitement. The non-stationary temperature distributions are studied for the long, short and middle impulse excitement.

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41

Oruc, Sertac. "Non-stationary Investigation of Extreme Rainfall." Civil Engineering Journal 7, no. 9 (September 1, 2021): 1620–33. http://dx.doi.org/10.28991/cej-2021-03091748.

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Natural or human-induced variability emerged from investigation of the traditional stationary assumption regarding extreme precipitation analyses. The frequency of extreme rainfall occurrence is expected to increase in the future and neglecting these changes will result in the underestimation of extreme events. However, applications of extremes accept the stationarity that assumes no change over time. Thus, non-stationarity of extreme precipitation of 5, 10, 15, and 30 minutes and 1-, 3-, 6-, and 24-hour data of 17 station in the Black Sea region were investigated in this study. Using one stationary and three non-stationary models for every station and storm duration, 136 stationary and 408 non-stationary models were constructed and compared. The results are presented as non-stationarity impact maps across the Black Sea Region to visualize the results, providing information about the spatial variability and the magnitude of impact as a percentage difference. Results revealed that nonstationary (NST) models outperformed the stationary model for almost all precipitation series at the 17 stations. The model in which time dependent location and scale parameter used (Model 1), performed better among the three different time variant non-stationary models (Model 1 as time variant location and scale parameters, Model 2 as time variant location parameter, and Model 3 as time variant scale parameter). Furthermore, non-stationary impacts exhibited site-specific behavior: Higher magnitudes of non-stationary impacts were observed for the eastern Black Sea region and the coastal line. Moreover, the non-stationary impacts were more explicit for the sub-hourly data, such as 5 minutes or 15 minutes, which can be one of the reasons for severe and frequent flooding events across the region. The results of this study indicate the importance of the selected covariate and the inclusion of it for the reliability of the model development. Spatial and temporal distribution of the nonstationary impacts and their magnitude also urges to further investigation of the impact on precipitation regime, intensification, severity. Doi: 10.28991/cej-2021-03091748 Full Text: PDF

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42

Barnes, John A., and Richard Meili. "A stationary Poisson departure process from a minimally delayed infinite server queue with non-stationary Poisson arrivals." Journal of Applied Probability 34, no. 3 (September 1997): 767–72. http://dx.doi.org/10.2307/3215101.

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The points of a non-stationary Poisson process with periodic intensity are independently shifted forward in time in such a way that the transformed process is stationary Poisson. The mean shift is shown to be minimal. The approach used is to consider an Mt/Gt/∞ queueing system where the arrival process is a non-stationary Poisson with periodic intensity function. A minimal service time distribution is constructed that yields a stationary Poisson departure process.

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43

Barnes, John A., and Richard Meili. "A stationary Poisson departure process from a minimally delayed infinite server queue with non-stationary Poisson arrivals." Journal of Applied Probability 34, no. 03 (September 1997): 767–72. http://dx.doi.org/10.1017/s002190020010141x.

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Анотація:

The points of a non-stationary Poisson process with periodic intensity are independently shifted forward in time in such a way that the transformed process is stationary Poisson. The mean shift is shown to be minimal. The approach used is to consider an Mt/Gt/∞ queueing system where the arrival process is a non-stationary Poisson with periodic intensity function. A minimal service time distribution is constructed that yields a stationary Poisson departure process.

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44

Masingi, Vusi Ntiyiso, and Daniel Maposa. "Modelling Long-Term Monthly Rainfall Variability in Selected Provinces of South Africa: Trend and Extreme Value Analysis Approaches." Hydrology 8, no. 2 (April 23, 2021): 70. http://dx.doi.org/10.3390/hydrology8020070.

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Extreme rainfall events have made significant damages to properties, public infrastructure and agriculture in some provinces of South Africa notably in KwaZulu-Natal and Gauteng among others. The general global increase in the frequency and intensity of extreme precipitation events in recent years is raising a concern that human activities might be heavily disturbed. This study attempts to model long-term monthly rainfall variability in the selected provinces of South Africa using various statistical techniques. The study investigates the normality and stationarity of the underlying distribution of the whole body of rainfall data for each selected province, the long-term trends of the rainfall data and the extreme value distributions which model the tails of the rainfall distribution data. These approaches were meant to help achieve the broader purpose of this study of investigating the long-term rainfall trends, stationarity of the rainfall distributions and extreme value distributions of monthly rainfall records in the selected provinces of South Africa in this era of climate change. The five provinces considered in this study are Eastern Cape, Gauteng, KwaZulu-Natal, Limpopo and Mpumalanga. The findings revealed that the long-term rainfall distribution for all the selected provinces does not come from a normal distribution. Furthermore, the monthly rainfall data distribution for the majority of the provinces is not stationary. The paper discusses the modelling of monthly rainfall extremes using the non-stationary generalised extreme value distribution (GEVD) which falls under the block maxima extreme value theory (EVT) approach. The maximum likelihood estimation method was used to obtain the estimates of the parameters. The stationary GEVD was found as the best distribution model for Eastern Cape, Gauteng, and KwaZulu-Natal provinces. Furthermore, model fitting supported non-stationary GEVD model for maximum monthly rainfall with nonlinear quadratic trend in the location parameter and a linear trend in the scale parameter for Limpopo, while in Mpumalanga the non-stationary GEVD model with a nonlinear quadratic trend in the scale parameter and no variation in the location parameter fitted well to the monthly rainfall data. The negative values of the shape parameters for Eastern Cape and Mpumalanga suggest that the data follow the Weibull distribution class, while the positive values of the shape parameters for Gauteng, KwaZulu-Natal and Limpopo suggest that the data follow the Fréchet distribution class. The findings from this paper could give information that can assist decision makers establish strategies for proper planning of agriculture, infrastructure, drainage system and other water resource applications in the South African provinces.

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45

Baldan, Damiano, Elisa Coraci, Franco Crosato, Maurizio Ferla, Andrea Bonometto, and Sara Morucci. "Importance of non-stationary analysis for assessing extreme sea levels under sea level rise." Natural Hazards and Earth System Sciences 22, no. 11 (November 14, 2022): 3663–77. http://dx.doi.org/10.5194/nhess-22-3663-2022.

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Abstract. Increased coastal flooding caused by extreme sea levels (ESLs) is one of the major hazards related to sea level rise. Estimates of return levels obtained under the framework provided by extreme-event theory might be biased under climatic non-stationarity. Additional uncertainty is related to the choice of the model. In this work, we fit several extreme-value models to two long-term sea level records from Venice (96 years) and Marseille (65 years): a generalized extreme-value (GEV) distribution, a generalized Pareto distribution (GPD), a point process (PP), the joint probability method (JPM), and the revised joint probability method (RJPM) under different detrending strategies. We model non-stationarity with a linear dependence of the model's parameters on the mean sea level. Our results show that non-stationary GEV and PP models fit the data better than stationary models. The non-stationary PP model is also able to reproduce the rate of extremes occurrence fairly well. Estimates of the return levels for non-stationary and detrended models are consistently more conservative than estimates from stationary, non-detrended models. Different models were selected as being more conservative or having lower uncertainties for the two datasets. Even though the best model is case-specific, we show that non-stationary extremes analyses can provide more robust estimates of return levels to be used in coastal protection planning.

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46

Schladitz, Katja. "Estimation of the intensity of stationary flat processes." Advances in Applied Probability 32, no. 01 (March 2000): 114–39. http://dx.doi.org/10.1017/s0001867800009800.

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The intensity of a stationary process of k-dimensional affine subspaces (k-flats) of ℝ d with directional distribution from a given family R is estimated by observing the process in a compact window. To this end we introduce a type of unbiased estimator (the R-estimator) using the available information about the directional distribution. Special cases are estimators for the intensity of stationary k-flat processes (1) with known directional distribution, (2) with directional distribution invariant with respect to a subgroup of the group of rotations in ℝ d and (3) with unknown directional distribution. We give sufficient conditions for the R-estimator to be the uniformly best unbiased estimator for the intensity of stationary Poisson k-flat processes with directional distribution in R. Equivalent statements for certain types of stationary Cox flat processes can be deduced directly from the results in the Poisson case. Moreover, we consider stationary ergodic flat processes with directional distribution in R and general stationary flat processes with unknown directional distribution, all with a non-degeneracy property. In both cases our estimator turns out to be the uniformly best unbiased estimator from a restricted set of estimators. The result for general stationary flat processes is proved with the help of a factorization result for the second factorial moment measure.

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47

Littlejohn, R. P. "A reversibility relationship for two Markovian time series models by stationary exponential tailed distribution." Journal of Applied Probability 31, no. 2 (June 1994): 575–81. http://dx.doi.org/10.2307/3215050.

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Анотація:

The continuous autoregressive and minification stationary non-negative time series models discussed by Chernick et al. (1988) are generalized to model marginal distributions which have atoms of mass at zero. The reversibility theorem relating these processes with exponential marginal distributions is extended to the case where the marginal distribution has exponential tail.

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48

Littlejohn, R. P. "A reversibility relationship for two Markovian time series models by stationary exponential tailed distribution." Journal of Applied Probability 31, no. 02 (June 1994): 575–81. http://dx.doi.org/10.1017/s0021900200045095.

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Анотація:

The continuous autoregressive and minification stationary non-negative time series models discussed by Chernick et al. (1988) are generalized to model marginal distributions which have atoms of mass at zero. The reversibility theorem relating these processes with exponential marginal distributions is extended to the case where the marginal distribution has exponential tail.

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49

Koh, S. K., C. H. Chin, Y. F. Tan, L. E. Teoh, A. H. Pooi, and Y. K. Goh. "Stationary queue length of a single-server queue with negative arrivals and nonexponential service time distributions." MATEC Web of Conferences 189 (2018): 02006. http://dx.doi.org/10.1051/matecconf/201818902006.

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Анотація:

In this paper, a single-server queue with negative customers is considered. The arrival of a negative customer will remove one positive customer that is being served, if any is present. An alternative approach will be introduced to derive a set of equations which will be solved to obtain the stationary queue length distribution. We assume that the service time distribution tends to a constant asymptotic rate when time t goes to infinity. This assumption will allow for finding the stationary queue length of queueing systems with non-exponential service time distributions. Numerical examples for gamma distributed service time with fractional value of shape parameter will be presented in which the steady-state distribution of queue length with such service time distributions may not be easily computed by most of the existing analytical methods.

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50

Mudersbach, Christoph, and Juergen Jensen. "AN ADVANCED STATISTICAL EXTREME VALUE MODEL FOR EVALUATING STORM SURGE HEIGHTS CONSIDERING SYSTEMATIC RECORDS AND SEA LEVEL RISE SCENARIO." Coastal Engineering Proceedings 1, no. 32 (January 29, 2011): 23. http://dx.doi.org/10.9753/icce.v32.currents.23.

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Анотація:

In this paper, a non-stationary extreme value analysis approach is introduced in order to determine coastal design water levels for future time horizons. The non-stationary statistical approach is based on the Generalized Extreme Value (GEV) distribution and a L-Moment parameter estimation as well as a Maximum-Likelihood-estimation. An additional approach considers sea level rise scenarios in the non-stationary extreme value analysis. All the methods are applied to the annual maximum water levels from 1849-2007 at the German North Sea gauge at Cuxhaven. The results show, that the non-stationary GEV approach is suitable for determining coastal design water levels.

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