Probability Distributions In Order Research Articles

Empirical Testing of Models of Autoregressive Conditional Heteroscedasticity Used for Prediction of the Volatility of Bulgarian Investment Funds

The relevance of the development is determined by the possibility of testing a complex analytical methodology for forecasting the daily volatility of Bulgarian investment funds, which will support the investment community in making adequate investment decisions. The used risk attribution quantification models GARCH (1.1), EGARCH (1.1), GARCH-M (1.1) and TGARCH (1.1) are adapted to predict the volatility of investment funds. The current development focuses on forecasting the risk concentration of investment funds (in Bulgaria) through the testing of complex, analytical and specialized models from the GARCH group. The object of the study includes quantitative analysis, estimation and forecasting of daily volatility through the models GARCH, EGARCH, GARCH-M and TGARCH with specification (1.1). The research covers the net balance sheet value of forty-two investment funds for the period from 13 July 2020 to 13 July 2023, where the results of the research show that according to three of the models GARCH, EGARCH and GARCH-M with the highest risk concentration the investment fund “Golden Lev Index 30” stands out. An exception to the thus formed trend is related to the TGARCH model in which the future conditional volatility is with the “EF Rapid” investment fund. When testing the models, we found that the GARCH model and the EGARCH model successfully optimize the regression parameters of the final equation for all analyzed investment funds, and as a result, valid forecasts are formed. In the case of the remaining two GARCH-M and TGARCH models, the impossibility of applicability of the model for some investment funds was found because of the optimization procedure, in which the parameters of the models have a value of zero. The present study is a unique mechanism for forecasting the daily volatility of Bulgarian investment funds, which further assists investors in risk assessment and is a prerequisite for making adequate and responsible investment decisions. The wide-spectrum toolkit of risk forecasting models allows their testing in investment funds with different risk natures (high-risk, balanced and low-risk). From a research point of view, in future research dedicated to modeling the risk attribution of investment funds, the analytical toolkit can be enriched with the following models: QGARCH, PGARCH, GJR-GARCH, IGARCH, SGARCH, AVGARCH, NGARCH and GAS. From a statistical point of view, we can apply the analyzed models to different probability distributions in order to describe the risky nature of investment funds.

Collective behavior of passive and active circle swimming particle mixtures.

We present a numerical study on a binary mixture of passive and circle swimming, self-propelling particles which interact via the Lennard-Jones (LJ) potential in two dimensions. Using Brownian Dynamics (BD) simulations, we present state diagrams using the control parameters such as attraction strength, angular velocity, self-propulsion velocity and composition. In a symmetric mixture, the system undergoes a transition from a mixed gel to a rotating passive cluster state and finally to a homogeneous fluid state as translational activity increases. The formation of the rotating cluster of passive particles surrounded by active and passive monomers is attributed to the combined effect of composition, activity and strength of attraction of the active particles. Different phases are characterized using radial distribution functions, bond order parameters, cluster fraction and probability distribution of local volume fractions. The present study addresses comprehensively the intricate role of activity, angular velocity, inter-particle interaction and compositional variation on the phase behavior. The predictions presented in the study can be experimentally realized in synthetic colloidal swimmers and motile bacterial suspensions.

Study on the stability of particle packing structure based on cells

The macroscopic mechanical property and the stability of granular mechanics system are determined by packing structure. Cells play a fundamental role in granular statistical mechanics and thus cells were utilized in this paper to research the packing structure of disk particles and gear particles in a two-dimensional cubic container. The probability distribution of cell order satisfies the exponential function distribution and is independent of intergranular friction, the size of system and vibration. Furthermore, it is observed that friction and system size are the key factors affecting the stability of particle packing structure. Significantly, the relationship between volume fraction and packing structure of disk particles is established under vibration. The experimental results reveal the characteristics of ordered packing structure of disordered particle system in mesoscale and provide data reference for perfecting the theory of particle mechanics.

Decentralized Data-Driven Load Restoration in Coupled Transmission and Distribution System With Wind Power

This paper proposes a new decentralized data-driven load restoration (DDLR) scheme for transmission and distribution (TD) systems with high penetration of wind power. Robust DDLR models are constructed in order to handle uncertainties and ensure the feasibility of decentralized schemes. The Wasserstein metric is used to describe the ambiguity sets of probability distributions in order to build the complete DDLR model and realize computationally tractable formulation. A data-driven model-nested analytical target cascading (DATC) algorithm is developed to obtain the final load restoration result by iteratively solving small-scale mathematical models. The proposed DDLR scheme provides load restoration results with adjustable robustness, and performance efficiency is independent from the amount of data. The DDLR scheme makes full use of the available data while respecting information privacy requirements of independent operated systems, and ensures the feasibility of a decentralized load restoration strategy even in the worst-case condition. The effectiveness of the proposed method is validated using a small-scale TD system and a large-scale system with the IEEE 118-bus TS and thirty IEEE-33 DSs, showing high computational efficiency and superior restoration performance.

Non-equilibrium response and slow equilibration in hard disk systems

The relaxation from a non-equilibrium state to the equilibrium depends on the methodologies and initial conditions. To investigate the microscopic mechanisms of equilibration systematically, we focus on the non-equilibrium response during the equilibration process induced by a disturbance of the homogeneous expansion of the simple hard disk systems. Large scale simulations by event-driven molecular dynamics revealed that an anomalous slow equilibration toward the liquid states emerges when starting from the co-existence phase. The origin of the slow decay mechanism is investigated using the probability distribution of local density and orientational order parameter.Their inhomogeneities seem to cause the anomalous slow equilibration.

Brownian Swarm Dynamics and Burgers’ Equation with Higher Order Dispersion

The concept of ranked order probability distribution unveils natural probabilistic interpretations for the kink waves (and hence the solitons) solving higher order dispersive Burgers’ type PDEs. Thanks to this underlying structure, it is possible to propose a systematic derivation of exact solutions for PDEs with a quadratic nonlinearity of the Burgers’ type but with arbitrary dispersive orders. As illustrations, we revisit the dissipative Kotrweg de Vries, Kuramoto-Sivashinski, and Kawahara equations (involving third, fourth, and fifth order dispersion dynamics), which in this context appear to be nothing but the simplest special cases of this infinitely rich class of nonlinear evolutions.

Regression models to dependence for exceedance

Extreme Value Theory (EVT) aims to study the tails of probability distributions in order to measure and quantify extreme events of maximum and minimum. In river flow data, an extreme level of a river may be related to the level of a neighboring river that flows into it. In this type of data, it is very common for flooding of a location to have been caused by a very large flow from an affluent river that is tens or hundreds of kilometers from this location. In this sense, an interesting approach is to consider a conditional model for the estimation of a multivariate model. Inspired by this idea, we propose a Bayesian model to describe the dependence of exceedance between rivers, where we considered a conditionally independent structure. In this model, the dependence between rivers is captured by modeling the excess marginally of one river as a consequence of linear functions of the other rivers. The results showed that there is a strong and positive connection between excesses in one river caused by the excesses of the other rivers.

Real-space renormalization for disordered systems at the level of large deviations

The real-space renormalization procedures on hierarchical lattices have been much studied for many disordered systems in the past at the level of their typical fluctuations. In the present paper, the goal is to analyze instead the renormalization flows for the tails of probability distributions in order to extract the scalings of their large deviations and the tails behaviors of the corresponding rate functions. We focus on the renormalization rule for the ground-state energy of the directed polymer model in a random medium, and study the various renormalization flows that can emerge for the tails as a function of the tails of the initial condition.

Football matches: Decision making in betting

AbstractThe aim of this paper is to approach the teaching of the Poisson distribution in a friendly and amusing way. It constitutes a common practice to adopt the main probability distributions in order to predict results of sport events and to estimate the win return of betting activities (Chalikias 2009). In particular, by using the Poisson distribution, we can calculate the probability of the final score in a football match, and then we can compare this probability with the values that various betting companies offer. Combining this information with the average of goals for both, it is possible to make a decision as to which betting company is more profitable for the betting players. The case study of the English Premier League is examined.

Real-time assessment and prediction on maritime risk state on the Arctic Route

ABSTRACTRecently, the Arctic Route has become busier with the continuous melting of Arctic ice. However, navigation on the Arctic Route would be much more complex than in normal water as harsh environmental conditions, such as ice-covered water and scarce costal ports that may cause more uncertainty. Nowadays, with the rapid development of sensors on board, more related data has become available. Thus, implementing comprehensive Arctic maritime risk assessment is urgent and necessary in practice. This study proposes an Arctic maritime risk state assessment method including real-time risk state assessment and risk prediction. Specifically, real-time observation samples’ numerical risk state would be firstly obtained with projection pursuit method from 10 risk indicators. Due to the fuzzy uncertainty of single observation set, information diffusion would be applied to provide diffusion estimation on risk probability distribution in order to depict risk state precisely. Also, the accumulated distribution can be regarded as the risk prediction for next time slot and risk entropy is introduced to depict risk tendency directly. Case study based on ‘Yongsheng’ is conducted to demonstrate and verify the effectiveness of the proposed method. The findings can be useful for the operators and management on board during the Arctic voyage.

Heisenberg's uncertainty conditions for various higher order probability distribution functions based on Budiyono–Rohrlich statistical model of quantum mechanics

This report discusses the explicit form of Heisenberg's uncertainty conditions based on recently proposed Budiyono–Rohrlich quantum interpretation which is formulated in terms of modified classical statistical mechanics within the framework of Hamilton–Jacobi formalism. This new statistical interpretation of quantum mechanics is remarkably compatible with the Copenhagen interpretation. We consider various probability distribution functions in the form of symmetric and localized higher order Gaussian, Cauchy-Lorentz and t− distribution functions. The characteristics of all those higher order distribution functions and the related uncertainty conditions are discussed, and we show that all those conditions satisfy the Heisenberg–Kennard uncertainty relation, as expected.

Bi-directional dominance for measure modeled uncertainty

Our objective here is to provide a formulation for a dominance relationship between variables having uncertain values, represented by measures, which can be used for ordering these uncertain values. We first discuss the use of monotonic set functions, fuzzy measures, for the representation of uncertain information. We consider the issue of comparing and ordering variables whose values are uncertain and represented via a measure and we suggest the use of bi-directional dominance, which can be seen as a generalization of stochastic dominance that is used to order probability distributions. We note the establishment of a dominance relationship between uncertain values is often not possible. In order to circumvent this we introduce the idea of surrogates for bi-directional dominance, here we associate with each uncertain value, measure, a scalar value that provides an ordering between all uncertain values. These surrogates are defined so that they maintain any relationship between measures that can be established with the use of bi-directional dominance.

Intermittency and stochastic modeling of hydrodynamic pressure fluctuations in the near field of compressible jets

The intermittent statistics of the pressure fluctuations measured in the near field of a compressible jet are investigated under several flow conditions. An experiment is carried out in a semi-anechoic chamber on a single stream compressible jet at Mach numbers varying from 0.5 to 0.9 and measuring the fluctuating pressure in several positions in the near field. The main quantities analyzed are the intermittent time and the energy amplitude of events that are extracted from the experimental data through a wavelet-based tracking algorithm. As an extension of a previous paper (Camussi et al., 2017), low order statistical moments (mean and variance) and Probability Distribution Functions are parametrized in terms of three relevant quantities characterizing the jet flow physics: the Mach number, the radial distance from the jet axis and the axial position. It is observed that the non-dimensional statistical quantities are weakly dependent upon the flow conditions allowing for simple stochastic models to be introduced on the basis of suitable fittings of averaged statistical properties and of the Probability Distribution Functions.

Fast-NPS—A Markov Chain Monte Carlo-based analysis tool to obtain structural information from single-molecule FRET measurements

The analysis tool and software package Fast-NPS can be used to analyse smFRET data to obtain quantitative structural information about macromolecules in their natural environment. In the algorithm a Bayesian model gives rise to a multivariate probability distribution describing the uncertainty of the structure determination. Since Fast-NPS aims to be an easy-to-use general-purpose analysis tool for a large variety of smFRET networks, we established an MCMC based sampling engine that approximates the target distribution and requires no parameter specification by the user at all. For an efficient local exploration we automatically adapt the multivariate proposal kernel according to the shape of the target distribution. In order to handle multimodality, the sampler is equipped with a parallel tempering scheme that is fully adaptive with respect to temperature spacing and number of chains. Since the molecular surrounding of a dye molecule affects its spatial mobility and thus the smFRET efficiency, we introduce dye models which can be selected for every dye molecule individually. These models allow the user to represent the smFRET network in great detail leading to an increased localisation precision. Finally, a tool to validate the chosen model combination is provided. Programme summaryProgramme Title : Fast-NPSProgramme Files doi:http://dx.doi.org/10.17632/7ztzj63r68.1Licencing provisions: Apache-2.0Programming language: GUI in MATLAB (The MathWorks) and the core sampling engine in C++Nature of problem: Sampling of highly diverse multivariate probability distributions in order to solve for macromolecular structures from smFRET data.Solution method: MCMC algorithm with fully adaptive proposal kernel and parallel tempering scheme.

The role of correlations in uncertainty quantification of transportation relevant fuel models

Large reaction mechanisms are often used to describe the combustion behavior of transportation-relevant fuels like gasoline, where these are typically represented by surrogate blends, e.g., n-heptane/iso-octane/toluene. We describe efforts to quantify the uncertainty in the predictions of such mechanisms at realistic engine conditions, seeking to better understand the robustness of the model as well as the important reaction pathways and their impacts on combustion behavior. In this work, we examine the importance of taking into account correlations among reactions that utilize the same rate rules and those with multiple product channels on forward propagation of uncertainty by Monte Carlo simulations. Automated means are developed to generate the uncertainty factor assignment for a detailed chemical kinetic mechanism, by first uniquely identifying each reacting species, then sorting each of the reactions based on the rate rule utilized. Simulation results reveal that in the low temperature combustion regime for iso-octane, the majority of the uncertainty in the model predictions can be attributed to low temperature reactions of the fuel sub-mechanism. The foundational, or small-molecule chemistry (C0C4) only contributes significantly to uncertainties in the predictions at the highest temperatures (Tc=900K). Accounting for correlations between important reactions is shown to produce non-negligible differences in the estimates of uncertainty. Including correlations among reactions that use the same rate rules increases uncertainty in the model predictions, while accounting for correlations among reactions with multiple branches decreases uncertainty in some cases. Significant non-linear response is observed in the model predictions depending on how the probability distributions of the uncertain rate constants are defined. It is concluded that care must be exercised in defining these probability distributions in order to reduce bias, and physically unrealistic estimates in the forward propagation of uncertainty for a range of UQ activities.

Perceiving safety risk of buildings adjacent to tunneling excavation: An information fusion approach

Abstract This paper develops a novel hybrid information fusion approach that integrates cloud model (CM), Dempster–Shafer (D–S) evidence theory and Monte Carlo (MC) simulation technique to perceive safety risk of tunnel-induced building damage under uncertainty. The correlation measurement in the CM framework is used to construct basic probability assignments (BPAs) within different risk states of input factors. An improved combination rule that incorporates the Dempster' rule and the weighted mean rule is used to deal with multi-source evidence with conflicts. The MC technique is used to simulate the input observation by using probability distribution in order to describe and reduce underlying uncertainty during the characterization and measurement of input factors. A multi-layer information fusion framework is proposed for the safety risk perception, with both hard data and soft data taken into account. Four buildings adjacent to the excavation of one tunnel section in Wuhan metro system in China are utilized as a case study to demonstrate the effectiveness and applicability of the developed approach. Results indicate that the developed approach is capable of (i) synthesizing multi-source information to achieve a more accurate result for safety risk perception, and (ii) identifying global sensitivities of input factors under uncertainty. Reliability of safety risk perception results is further tested under different scenarios with different bias levels in the measurement of input factors, and the developed approach proves to have a strong robustness and fault-tolerant capacity. This approach can be used by practitioners in the industry as a decision tool to perceive and anticipate the potential safety risks in tunneling projects.

Impact of Hydrological Uncertainty on Water Management Decisions

This study focuses on the analysis of uncertainties in hydrologic series and their impact on water resources management decisions. The methodology is based on Monte Carlo simulation, where relevant parameters on the rainfall-runoff processes of a hydrologic model were sampled from suitable probability distributions in order to analyse the probability distribution of output variables in a water resources system model. The procedure was applied to three water resources systems in the Duero basin (Spain). Results showed that the performances of the water resources systems are very sensitive to uncertainties in the model input. The deviation from the reliabilities or cumulated supply deficits obtained in the water resources systems compared to the reference inflows was much larger when the perturbations were unfavourable than when they were favourable. This suggests that the uncertainty analysis may have important implications when using these performance measures of the water resources system in decision making, particularly in dry years. The uncertainty on hydrologic variables may change dramatically our assessment of the performance of a water resources system and thus hydrologic inputs should be evaluated with extreme care.

A robust scheme for distributed particle filtering in wireless sensors networks

Wireless sensor networks (WSNs) have become a popular technology for a broad range of applications where the goal is to track and forecast the evolution of time-varying physical magnitudes. Several authors have investigated the use of particle filters (PFs) in this scenario. PFs are very flexible, Monte Carlo based algorithms for tracking and prediction in state-space dynamical models. However, to implement a PF in a WSN, the algorithm should run over different nodes in the network to produce estimators based on locally collected data. These local estimators then need to be combined so as to produce a global estimator. Existing approaches to the problem are either heuristic or well-principled but impractical (as they impose stringent conditions on the WSN communication capacity). Here, we introduce a novel distributed PF that relies on the computation of median posterior probability distributions in order to combine local Bayesian estimators (obtained at different nodes) in a way that is efficient, both computation and communication-wise. An extensive simulation study for a target tracking problem shows that the proposed scheme is competitive with existing consensus-based distributed PFs in terms of estimation accuracy, while it clearly outperforms these methods in terms of robustness and communication requirements.

Evaluating Choquet Integrals Whose Arguments are Probability Distributions

We describe the use of the Choquet integral for finding a mean-like aggregated value of a collection of arguments with respect to a fuzzy measure. We observe the need for ordering the arguments in using this integral. We consider the case where the arguments being aggregated are random variables, probability distributions. In this case, we are faced with the problem of having to order probability distributions. Given the difficulty of obtaining a linear ordering over a collection of probability distributions, we must search for other methods for obtaining a Choquet type aggregation of a collection of probability distributions that does not require a linear ordering; we refer to these as surrogates. Here, we provide one surrogate for calculating the Choquet integral in the case where the objects being aggregated are probability distributions called the probabilistic exceedance method.

Validation of multivariate classification methods using analytical fingerprints – concept and case study on organic feed for laying hens

Multivariate classification methods based on analytical fingerprints have found many applications in the food and feed area, but practical applications are still scarce due to a lack of a generally accepted validation procedure. This paper proposes a new approach for validation of this type of methods. A part of the validation procedure requires a description of qualitative aspects: the method’s goal and purpose and adequateness of the sample sets used. The required quantitative performance is assessed from probabilistic data. Probability distributions are generalized using kernel density estimates, which allow meaningful interpolation and direct comparison and combination of different distributions. We propose inclusion of a permutation test, and provide suggestions for the assessment of the analytical repeatability in the method’s probabilistic units. The latter can serve as a quality control measure. For assessment of the method’s overall performance, we propose to apply the combined cross validation and external validation set probability distributions in order to obtain the best estimate for the method’s performance on future samples. Qualitative and quantitative aspects are to be combined into a validation dossier stating performance for a well-defined purpose and scope. The proposed validation approach is applied to a case study: a binary classification discriminating organic from conventional laying hen feed based on fatty acid profiling that is essential to ensure the organic status of eggs for human consumption. For this case study, an expected accuracy for organic feed recognition of 96% is obtained for an explicitly defined scope.