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For two-component mixtures of shifted distributions a general formula for finding the value of the shift parameter ã0,s, at which the cumulant coefficients γs ( p ã) of any order s ≥ 3 are equal to zero, is obtained. An algorithm for mathematical and computer modeling of two component mixtures of shifted distributions with zero cumulant coefficients is formulated. General formulas for two-component mixtures of shifted gamma-distributions with zero cumulant coefficients of any order are obtained and examples of mixtures with zero skewness and kurtosis coefficients are given. General formulas of two-component mixtures of shifted Student’s distributions with zero cumulant coefficients of any order are obtained and examples of mixtures with zero kurtosis coefficient and coefficient γ6 ( p, ã) are given. The research results provide the practical possibility of using two-component mixtures of shifted distributions for mathematical and computer modeling of non-Gaussian random variables with zero cumulant coefficients of any order. [ABSTRACT FROM AUTHOR]

The dependence of the extremes and zeros of the excess kurtosis γ4(p, ã ) on the weight coefficient P is researched. Formulas for finding the extrema points, the values of the minimums and maximums of the excess kurtosis are obtained. Conditions on the shift parameter ã under which the extrema points belong to the interval [0;1] are determined. Formulas for finding the zeros of the excess kurtosis are obtained and conditions on shift parameter under which the roots of the equation γ4(p, ã ) are real and belong to the interval [0;1] are determined. Examples of calculating extremes and zeros of the excess kurtosis of two-component mixtures of shifted non-Gaussian distributions are considered. The results of the research justify the possibility of practical application of two-component mixtures of shifted distributions for mathematical and computer modeling of an infinite number of non-Gaussian random variables with negative, positive and zero excess kurtosis. [ABSTRACT FROM AUTHOR]

Extensive high-speed railway (HSR) network resembled the intricate vascular system of the human body, crisscrossing mainlands. Seismic events, known for their unpredictability, pose a significant threat to both trains and bridges, given the HSR's extended operational duration. Therefore, ensuring the running safety of train-bridge coupled (TBC) system, primarily composed of simply supported beam bridges, is paramount. Traditional methods like the Monte Carlo method fall short in analyzing this intricate system efficiently. Instead, efficient algorithm like the new point estimate method combined with moment expansion approximation (NPEM-MEA) is applied to study random responses of numerical simulation TBC systems. Validation of the NPEM-MEA's feasibility is conducted using the Monte Carlo method. Comparative analysis confirms the accuracy and efficiency of the method, with a recommended truncation order of four to six for the NPEM-MEA. Additionally, the influences of seismic magnitude and epicentral distance are discussed based on the random dynamic responses in the TBC system. This methodology not only facilitates seismic safety assessments for TBC systems but also contributes to standard-setting for these systems under earthquake conditions. [ABSTRACT FROM AUTHOR]

This paper presents a methodology for computing Value at Risk for financial assets that does not follow a normal distribution of return. A back-testing approach have been applied in order to select the best theoretical non-Gaussian distributions that can explain the behavior of the empirical data. In this study, Cauchy, Laplace, Logistic and Beta distributions have been considered. As benchmark, historical distribution, and Extreme Value Theory (EVT) method have been used. The experiment suggests differences in estimation of over 5 times between one method and another. [ABSTRACT FROM AUTHOR]

The estimation of higher-order co-moments of asset returns play an important role in higher-order moment portfolio selection. We improve the estimation of higher-order co-moments by using non-Gaussian components in the observed factor models and construct a portfolio selection method, labelled as Non-Gaussian Component (NGC) portfolio. We assume the non-normality of asset returns is driven by the independent non-Gaussian components in the observed factors. Through identifying and extracting those non-Gaussian components, the parameters in the portfolio objective function have been significantly decreased. We show that the non-Gaussian components can be estimated consistently by the independent component analysis and higher-order cumulant tests. Simulation studies confirm the good finite sample properties of our estimation procedure and further the performance of the NGC portfolio. Empirical results show that the NGC portfolio outperforms the benchmark portfolios, and only a few non-Gaussian components are needed to optimize the objective function. [ABSTRACT FROM AUTHOR]

The dependence of the cumulant coefficients of two-component mixtures of shifted nonGaussian distributions on the weight coefficient is analyzed and conditions are determined under which the cumulant coefficients of any orders are equal to zero. The dependence of the cumulant coefficients of two-component mixtures on the shear parameter is investigated and the parameter values are determined at which the cumulant coefficients of any orders have extrema and zeros. The dependence of the skewness and excess kurtosis of a two-component mixture of shifted Gumbel distributions of type 1 on the weight coefficient and the shear parameter is investigated and their values are obtained at which the skewness and excess kurtosis of the mixture are equal to zero. The features of computer modeling of random variables, the probability density of which is a two-component mixture of shifted distributions, are considered. [ABSTRACT FROM AUTHOR]

• Pairwise coupling of Nataf-based stochastic models through disaggregation. • Generation of multi-scale timeseries with any distribution and correlation structure. • Applicable for multivariate disaggregation/simulation problems. The generation of hydrometeorological time series that exhibit a given probabilistic and stochastic behavior across multiple temporal levels, traditionally expressed in terms of specific statistical characteristics of the observed data, is a crucial task for risk-based water resources studies, and simultaneously a puzzle for the community of stochastics. The main challenge stems from the fact that the reproduction of a specific behavior at a certain temporal level does not imply the reproduction of the desirable behavior at any other level of aggregation. In this respect, we first introduce a pairwise coupling of Nataf-based stochastic models within a disaggregation scheme, and next we propose their puzzle-type configuration to provide a generic stochastic simulation framework for multivariate processes exhibiting any distribution and any correlation structure. Within case studies we demonstrate two characteristic configurations, i.e., a three-level one, operating at daily, monthly and annual basis, and a two-level one to disaggregate daily to hourly data. The first configuration is applied to generate correlated daily rainfall and runoff data at the river basin of Achelous, Western Greece, which preserves the stochastic behavior of the two processes at the three temporal levels. The second configuration disaggregates daily rainfall, obtained from a meteorological station at Germany, to hourly. The two studies reveal the ability of the proposed framework to represent the peculiar behavior of hydrometeorological processes at multiple temporal resolutions, as well as its flexibility on formulating generic simulation schemes. [ABSTRACT FROM AUTHOR]

Geostatistical analysis has been introduced over half a century ago to allow quantifying seemingly random spatial variations in earth quantities such as rock mineral content or permeability. The traditional approach has been to view such quantities as multivariate Gaussian random functions characterized by one or a few well-defined spatial correlation scales. There is, however, mounting evidence that many spatially varying quantities exhibit non-Gaussian behavior over a multiplicity of scales. The purpose of this minireview is not to paint a broad picture of the subject and its treatment in the literature. Instead, we focus on very recent advances in the recognition and analysis of this ubiquitous phenomenon, which transcends hydrology and the Earth sciences, brought about largely by our own work. In particular, we use porosity data from a deep borehole to illustrate typical aspects of such scalable non-Gaussian behavior, describe a very recent theoretical model that (for the first time) captures all these behavioral aspects in a comprehensive manner, show how this allows generating random realizations of the quantity conditional on sampled values, point toward ways of incorporating scalable non-Gaussian behavior in hydrologic analysis, highlight the significance of doing so, and list open questions requiring further research. [ABSTRACT FROM AUTHOR]

This article focuses on investigation of statistical approaches to the task of control performance assessment. Different statistical measures with Gaussian and non-Gaussian probabilistic distributions are taken into consideration. Analysis starts with the observations for simulated proportional–integral–derivative control error histograms followed by its statistical investigation using selected probabilistic distribution functions. Simulation experiments are followed by the analysis of control data originating from real industrial loops. Shadowing effect of long-tail control error histograms is identified, as it may significantly disable proper loop quality assessment. Results show that non-Gaussian approach with Cauchy or α-stable distributions seems to be reasonable assessment alternative in case of disturbances existing in industrial processes. [ABSTRACT FROM AUTHOR]

For many stochastic phenomena, we observe statistical distributions that have fat-tails and high-peaks compared to the Gaussian distribution. In this paper, we will explain how observable statistical distributions in the macroscopic world could be related to the randomness in the subatomic world. We show that fat-tailed (leptokurtic) phenomena in our everyday macroscopic world are ultimately rooted in Gaussian – or very close to Gaussian-distributed subatomic particle randomness, but they are not, in a strict sense, Gaussian distributions. By running a truly random experiment over a three and a half-year period, we observed a type of random behavior in trillions of photons. Combining our results with simple logic, we find that fat-tailed and high-peaked statistical distributions are exactly what we would expect to observe if the subatomic world is quantized and not continuously divisible. We extend our analysis to the fact that one typically observes fat-tails and high-peaks relative to the Gaussian distribution in stocks and commodity prices and many aspects of the natural world; these instances are all observable and documentable macro phenomena that strongly suggest that the ultimate building blocks of nature are discrete (e.g. they appear in quanta). [ABSTRACT FROM AUTHOR]

Uncertainty-aware design and management of urban water systems lies on the generation of synthetic series that should precisely reproduce the distributional and dependence properties of residential water demand process (i.e., significant deviation from Gaussianity, intermittent behaviour, high spatial and temporal variability and a variety of dependence structures) at various temporal and spatial scales of operational interest. This is of high importance since these properties govern the dynamics of the overall system, while prominent simulation methods, such as pulse-based schemes, address partially this issue by preserving part of the marginal behaviour of the process (e.g., low-order statistics) or neglecting the significant aspect of temporal dependence. In this work, we present a single stochastic modelling strategy, applicable at any fine time scale to explicitly preserve both the distributional and dependence properties of the process. The strategy builds upon the Nataf’s joint distribution model and particularly on the quantile mapping of an auxiliary Gaussian process, generated by a suitable linear stochastic model, to establish processes with the target marginal distribution and correlation structure. The three real-world case studies examined, reveal the efficiency (suitability) of the simulation strategy in terms of reproducing the variety of marginal and dependence properties encountered in water demand records from 1-min up to 1-h.

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Distributions of data taken from crystal structure databases, display unusual statistical properties like non-Gaussian shape, polymodality, and heavy tails. These features, typical for statistics of numerical data in social systems, appear in bigger sets (from hundreds to many thousand points) of database-originated parameters. The non-classic statistics of physical data collected through many years reflects a strong impact of social factors (financial support, exchange of information, competition, etc.) on a research activity. The values of some definite structural parameter, determined (and deposited to a database) by different authors, generally are neither independent nor random; their handling by common statistical tools may result in incorrect conclusions and wrong predictions. These statements are illustrated by several sets of reliable structural data whose statistics looks 'bad,' or inconclusive, in contemporary structural chemistry. [ABSTRACT FROM AUTHOR]

The impact of the logconductivity ( Y = ln K ) distribution f Y on transport at the MADE site is analyzed. Our principal interest is in non-Gaussian f Y characterized by heavier tails than the Gaussian. Both the logconductivity moments and f Y itself are inferred, taking advantage of the detailed measurements of Bohling et al. (2012). The resulting logconductivity distribution displays heavier tails than the Gaussian, although the departure from Gaussianity is not significant. The effect of the logconductivity distribution on the breakthrough curve (BTC) is studied through an analytical, physically based model. It is found that the non-Gaussianity of the MADE logconductivity distribution does not strongly affect the BTC. Counterintuitively, assuming heavier tailed distributions for Y , with same variance, leads to BTCs which are more symmetrical than those for the Gaussian f Y , with less pronounced preferential flow. Results indicate that the impact of strongly non-Gaussian, heavy tailed distributions on solute transport in heterogeneous porous formations can be significant, especially in the presence of high heterogeneity, resulting in reduced preferential flow and retarded peak arrivals. [ABSTRACT FROM AUTHOR]

We consider random vectors drawn from a multivariate normal distribution and compute the sample statistics in the presence of stochastic correlations. For this purpose, we construct an ensemble of random correlation matrices and average the normal distribution over this ensemble. The resulting distribution contains a modified Bessel function of the second kind whose behavior differs significantly from the multivariate normal distribution, in the central part as well as in the tails. This result is then applied to asset returns. We compare with empirical return distributions using daily data from the NASDAQ Composite Index in the period from 1992 to 2012. The comparison reveals good agreement, the average portfolio return distribution describes the data well especially in the central part of the distribution. This in turn confirms our ansatz to model the nonstationarity by an ensemble average. [ABSTRACT FROM AUTHOR]

The Ensemble Kalman Filter (EnKF) is a Monte Carlo-based technique for assisted history matching and real-time updating of reservoir models. However, it often fails to detect precise locations of distinct facies boundaries and their proportions, as the facies distributions are non-Gaussian, while geologic data for reservoir modeling is usually insufficient. In this paper, a new re-sampling step is introduced to the conventional EnKF formulation; after certain number of assimilation steps, the updated ensemble is used to generate a new ensemble with a novel probability weighted re-sampling scheme. The new ensemble samples from a probability density function that is conditional to both the geological information and the early production data. After the re-sampling step, the forecast model is applied to the new ensemble from the beginning up to the last update step (without any intermediate Kalman updates). Full EnKF is again applied on the ensemble members to assimilate the remaining production history. Combination of EnKF and regenerating new members using the re-sampling method demonstrates reasonable improvement and reduction of uncertainty in history matching of reservoir models with multiple facies. The histogram and the experimental variogram of the updated ensemble members are more consistent with the static geologic information. Moreover, the technique helps maintaining ensemble variance which is essential for uncertainty estimation in the posterior probability distribution of facies proportions. [ABSTRACT FROM AUTHOR]

The general limit distributions of the sum of random variables described by a finite matrix product ansatz are characterized. Using a mapping to a Hidden Markov Chain formalism, non-standard limit distributions are obtained, and related to a form of ergodicity breaking in the underlying non-homogeneous Hidden Markov Chain. The link between ergodicity and limit distributions is detailed and used to provide a full algorithmic characterization of the general limit distributions. [ABSTRACT FROM AUTHOR]

In this work we propose a new and general approach to build dependence in multivariate Lévy processes. We fully characterize a multivariate Lévy process whose margins are able to approximate any Lévy type. Dependence is generated by one or more common sources of jump intensity separately in jumps of any sign and size and a parsimonious method to determine the intensities of these common factors is proposed. Such a new approach allows the calibration of any smooth transition between independence and a large amount of linear dependence and provides greater flexibility in calibrating nonlinear dependence than in other comparable Lévy models in the literature. The model is analytically tractable and a straightforward multivariate simulation procedure is available. An empirical analysis shows an accurate multivariate fit of stock returns in terms of linear and nonlinear dependence. A numerical illustration of multi-asset option pricing emphasizes the importance of the proposed new approach for modeling dependence. [ABSTRACT FROM PUBLISHER]

A realistic ARCH process is set up so as to duplicate, for all practical purposes, the properties of stock time series from 1 day to 1 year. The process includes heteroskedasticity with long memory, leverage, fat-tail innovations, relative return, price granularity, and holidays. Its adequacy to describe empirical data is controlled over a broad panel of statistics, including (robust L-statistics) skew, (robust) kurtosis, shape factor for the volatility distribution, and lagged correlations between combinations of return and volatility. These statistics are computed for returns and volatilities with characteristic time intervals ranging from 1 day to 1 year. This wide cross-check between stock time series and simulations ensures that the most important features of the data are correctly captured by the process up to 1 year. The by-products of the statistical analyses and estimations are (1) a positive skew, (2) a cross-sectional relation between kurtosis and heteroskedasticity, (3) a very similar cross-sectional distribution for the statistics evaluated over the empirical data set or for the process with one set of parameters and (4) the heteroskedasticity is very close to an integrated volatility process. [ABSTRACT FROM AUTHOR]

The precision of estimates of system performance and of parameters that affect the per-formance is often based upon the standard deviation obtained from the usual equation for the propagation of variances derived from a Taylor series expansion. With ever increasing computing power it is now possible to utilize the Bayesian hierarchical approach to yield improved estimates of the precision. Although quite popular in the sta-tistical community, the Bayesian approach has not been widely used in the heat transfer and fluid mechanics communities because of its complexity and subjectivity. The paper develops the necessary equations and applies them to Wo typical heat transfer problems, measurement of conductivity with heat losses and heat transfer from a fin. Because of the heat loss the probability distribution of the conductivity is far from Gaussian. Using this conductivity distribution for the fin gives a very long tailed distribution for the heat transfer from the fin. [ABSTRACT FROM AUTHOR]

The canonical process used to describe financial time series is based on a logarithmic random walk. Adding a fat-tail distribution for the innovations in this framework creates fundamental inconsistencies, essentially related to a diverging integral. The problems are related to (1) the (infinite) values of statistical quantities for processes with fat-tail innovations, (2) the robustness of computations when dealing with large events (genuine or noise), and (3) the pricing of options with heteroskedasticity and fat tails. Instead of logarithmic processes, we advocate using geometric processes and relative returns so that these problems do not occur. The mathematical properties of geometric processes are explored for setups of increasing complexity. For empirical time series and for processes, the skews are evaluated using a robust estimator and are compared for both return definitions. Finally, the European option pricing framework is modified to use geometric processes for the underlying, allowing the incorporation of natural fat-tail innovations. [ABSTRACT FROM AUTHOR]

This paper contributes to the characterization of the probability density of the price returns in some European day-ahead electricity markets (NordPool, APX, Powernext) by fitting flexible and general families of distributions, such as the α-stable, Normal Inverse Gaussian (NIG), Exponential Power (EP), and Asymmetric Exponential Power (AEP) distributions, and comparing their goodness of fit. The α-stable and the NIG systematically outperform the EP and AEP models, but the tail behavior and the skewness are sensitive to the definition of the returns and to the deseasonalization methods. In particular, the logarithmic transform and volatility rescaling tend to dampen the extreme returns. [ABSTRACT FROM AUTHOR]

We establish the large deviations asymptotic performance (error exponent) of consensus+innovations distributed detection over random networks with generic (non-Gaussian) sensor observations. At each time instant, sensors 1) combine theirs with the decision variables of their neighbors (consensus) and 2) assimilate their new observations (innovations). This paper shows for general non-Gaussian distributions that consensus+innovations distributed detection exhibits a phase transition behavior with respect to the network degree of connectivity. Above a threshold, distributed is as good as centralized, with the same optimal asymptotic detection performance, but, below the threshold, distributed detection is suboptimal with respect to centralized detection. We determine this threshold and quantify the performance loss below threshold. Finally, we show the dependence of the threshold and of the performance on the distribution of the observations: the asymptotic performance of distributed detectors over the same random network with different observations' distributions, for example, Gaussian, Laplace, or quantized, may be different, even though the asymptotic performance of the corresponding centralized detectors is the same. [ABSTRACT FROM PUBLISHER]

We describe financial systems as condensates, similar to Bose-Einstein condensates, and calculate equilibrium statistical distributions following from the model. The calculated distribution of investments into speculated financial asset is exponentially truncated Pareto distribution, and the calculated distribution of the price moves is exponentially truncated Levy distribution. The calculated from the model distributions correspond well to the empirically observed distributions.

In this paper we propose a novel Bayesian methodology for Value-at-Risk computation based on parametric Product Partition Models. Value-at-Risk is a standard tool for measuring and controlling the market risk of an asset or portfolio, and is also required for regulatory purposes. Its popularity is partly due to the fact that it is an easily understood measure of risk. The use of Product Partition Models allows us to remain in a Normal setting even in the presence of outlying points, and to obtain a closed-form expression for Value-at-Risk computation. We present and compare two different scenarios: a product partition structure on the vector of means and a product partition structure on the vector of variances. We apply our methodology to an Italian stock market data set from Mib30. The numerical results clearly show that Product Partition Models can be successfully exploited in order to quantify market risk exposure. The obtained Value-at-Risk estimates are in full agreement with Maximum Likelihood approaches, but our methodology provides richer information about the clustering structure of the data and the presence of outlying points. [ABSTRACT FROM AUTHOR]

The need for an accurate representation of tail risk has become increasingly acute in the wake of the credit crisis. We introduce a hyper-cuboid normal mixture copula that permits the representation of complex tail-dependence structures in a multi-dimensional setting. We outline an efficient pattern-recognition calibration methodology that can identify tail dependencies independent of the number of risk factors considered. This model is used to develop a new framework for pricing credit derivative instruments, and we derive semi-analytical and analytical pricing formulae for a first-to-default swap and illustrate with an example valuation. Model assumptions are validated against iTraxx Series 5 equity data over an 8-year period. Identification and representation of tail dependencies is crucial to further the study of contagion dynamics, and our model provides a basis for future research in this area. [ABSTRACT FROM AUTHOR]

Abstract: Atmospheric dispersion is a complex nonlinear physical process with numerous uncertainties in model parameters, inputs, source parameters, initial and boundary conditions. Accurate propagation of these uncertainties through the dispersion models is crucial for a reliable prediction of the probability distribution of the states and assessment of risk. A simple three-dimensional Gaussian puff-based dispersion model is used as a test case to study the effect of uncertainties in the model parameters and initial conditions on the output concentration. A polynomial chaos based approach is used to numerically investigate the evolution of the model output uncertainties due to initial condition and parametric uncertainties. The polynomial chaos solution is found to be an accurate approximation to ground truth, established by Monte Carlo simulation, while offering an efficient computational approach for large nonlinear systems with a relatively small number of uncertainties. [Copyright &y& Elsevier]

The Basel II framework allows the calculation of the capital requirements for market risk with Value-at-Risk models. Since no special model is prescribed in the framework, banks may use simple models with questionable assumptions concerning their underlying distributions. Our numerical analysis reveals that simple VaR models that perform noticeably worse than comparable simple models with more realistic assumptions may lead to a lower level of regulatory capital for banks. For this reason, banks have a major incentive to implement bad models. This is obviously contrary to the interests of regulatory authorities. [ABSTRACT FROM AUTHOR]

The quality of operational risk data sets suffers from missing or contaminated data points. This may lead to implausible characteristics of the estimates. Outliers, especially, can make a modeler's task difficult and can result in arbitrarily large capital charges. Robust statistics provides ways to deal with these problems as well as measures for the reliability of estimators. We show that using maximum likelihood estimation can be misleading and unreliable assuming typical operational risk severity distributions. The robustness of the estimators for the Generalized Pareto distribution, and the Weibull and Lognormal distributions is measured considering both global and local reliability, which are represented by the breakdown point and the influence function of the estimate. [ABSTRACT FROM AUTHOR]

In this paper, we develop a multivariate risk-neutral Levy process model and discuss its applicability in the context of the volatility smile of multiple assets. Our formulation is based upon a linear combination of independent univariate Levy processes and can easily be calibrated to a set of one-dimensional marginal distributions and a given linear correlation matrix. We derive conditions for our formulation and the associated calibration procedure to be well-defined and provide some examples associated with particular Levy processes permitting a closed-form characteristic function. Numerical results of the option premiums on three currencies are presented to illustrate the effectiveness of our formulation with different linear correlation structures. [ABSTRACT FROM AUTHOR]

As GARCH models and stable Paretian distributions have been revisited in the recent past with the papers of Hansen and Lunde (J Appl Econom 20: 873-889, 2005) and Bidarkota and McCulloch (Quant Finance 4: 256--265, 2004), respectively, in this paper we discuss alternative conditional distributional models for the daily returns of the US, German and Portuguese main stock market indexes, considering ARMA-GARCH models driven by Normal, Student's t and stable Paretian distributed innovations. We find that a GARCH model with stable Paretian innovations fits returns clearly better than the more popular Normal distribution and slightly better than the Student's t distribution. However, the Student's t outperforms the Normal and stable Paretian distributions when the out-of-sample density forecasts are considered. [ABSTRACT FROM AUTHOR]

The present paper studies the non-parametric estimation of volatility in financial time series. Support Vector Regression (SVR) is applied and compared with alternative techniques for estimating a Conditional Heteroskedastic AutoRegressive Nonlinear (CHARN) model. A multiscale decomposition analysis decomposes a time series into several scales, and then several separated SVRs, equal to the number of scales, are fed for running the CHARN model by scaled decomposed series. A multiscale CHARN model, which is an incorporation of wavelet decomposition analysis with a CHARN model estimated by SVR, is proposed and investigated using real-world data sets. To exploit the locality advantage of wavelets, we use wavelet analysis and combine it with SVR. Wavelets are able to economically describe phenomena that are heterogeneous. Recent studies on heterogeneous agents in financial markets theoretically support advocated scale-based analysis of markets, and, of course, the multiscale CHARN model proposition, since it is believed that each scale corresponds to each heterogeneous agent who acts differently in the market. Our objective is to improve the accuracy of estimation by applying multiscale decomposition. The results of applying SVR to estimate the CHARN model in a single resolution on real-world time series indicate that it outperforms the technical benchmarks. Also, the multiscale CHARN model estimated by SVR is more accurate than a single scale model. [ABSTRACT FROM AUTHOR]

We report on a study of the Tehran Price Index (TEPIX) from 2001 to 2006 as an emerging market that has been affected by several political crises during the recent years, and analyze the non-Gaussian probability density function (PDF) of the log returns of the stock prices. We show that while the average of the index did not fall very much over the time period of the study, its day-to-day fluctuations strongly increased due to the crises. Using an approach based on multiplicative processes with a detrending procedure, we study the scale-dependence of the non-Gaussian PDFs, and show that the temporal dependence of their tails indicates a gradual and systematic increase in the probability of the appearance of large increments in the returns on approaching distinct critical time scales over which the TEPIX has exhibited maximum uncertainty. [ABSTRACT FROM AUTHOR]

Abstract: Temperature maps of the cosmic microwave background (CMB) radiation, as those obtained by the Wilkinson microwave anisotropy probe (WMAP), provide one of the most precise data sets to test fundamental hypotheses of modern cosmology. One of these issues is related to the statistical properties of the CMB temperature fluctuations. We analysed here the WMAP data and found that the distribution of the CMB temperature fluctuations can be quite well fitted by the anomalous temperature distribution emerging within non-extensive statistical mechanics. This theory is based on the non-extensive entropy , with the Boltzmann–Gibbs expression as the limit case . For the frequencies investigated (, 60.8, and 93.5 GHz), we found that is well described by , with , which indicate, at the 99% confidence level, that Gaussian temperature distributions , corresponding to the limit, do not properly represent the CMB temperature fluctuations measured by WMAP. [Copyright &y& Elsevier]

We study a scenario under which variable step random walks give anomalous statistics. We begin by analyzing the Martingale Central Limit Theorem to find a sufficient condition for the limit distribution to be non-Gaussian. We study the case when the scaling index∼ζ is∼12. For corresponding continuous time processes, it is shown that the probability density function W( x; t) satisfies the Fokker–Planck equation. Possible forms for the diffusion coefficient are given, and related to W( x, t). Finally, we show how a time-series can be used to distinguish between these variable diffusion processes and Lévy dynamics. [ABSTRACT FROM AUTHOR]

The distribution of resistance fluctuations of conducting thin films with granular structure near electrical breakdown is studied by numerical simulations. The film is modeled as a resistor network in a steady state determined by the competition between two biased processes, breaking and recovery. Systems of different sizes and with different levels of internal disorder are considered. Sharp deviations from a Gaussian distribution are found near breakdown and the effect increases with the degree of internal disorder. We show that in general this non-Gaussianity is related to the finite size of the system and vanishes in the large size limit. Nevertheless, near the critical point of the conductor–insulator transition, deviations from Gaussianity persist when the size is increased and the distribution of resistance fluctuations is well fitted by the universal Bramwell–Holdsworth–Pinton distribution. [Copyright &y& Elsevier]

In this study, we propose a new bootstrap strategy to obtain prediction intervals for autoregressive integrated moving-average processes. Its main advantage over other bootstrap methods previously proposed for autoregressive integrated processes is that variability due to parameter estimation can be incorporated into prediction intervals without requiring the backward representation of the process. Consequently, the procedure is very flexible and can be extended to processes even if their backward representation is not available. Furthermore, its implementation is very simple. The asymptotic properties of the bootstrap prediction densities are obtained. Extensive finite-sample Monte Carlo experiments are carried out to compare the performance of the proposed strategy vs. alternative procedures. The behaviour of our proposal equals or outperforms the alternatives in most of the cases. Furthermore, our bootstrap strategy is also applied for the first time to obtain the prediction density of processes with moving-average components. [ABSTRACT FROM AUTHOR]

It is well known that time series of returns are characterized by volatility clustering and excess kurtosis. Therefore, when modelling the dynamic behavior of returns, inference and prediction methods, based on independent and/or Gaussian observations may be inadequate. As bootstrap methods are not, in general, based on any particular assumption on the distribution of the data, they are well suited for the analysis of returns. This paper reviews the application of bootstrap procedures for inference and prediction of financial time series. In relation to inference, bootstrap techniques have been applied to obtain the sample distribution of statistics for testing, for example, autoregressive dynamics in the conditional mean and variance, unit roots in the mean, fractional integration in volatility and the predictive ability of technical trading rules. On the other hand, bootstrap procedures have been used to estimate the distribution of returns which is of interest, for example, for Value at Risk (VaR) models or for prediction purposes. Although the application of bootstrap techniques to the empirical analysis of financial time series is very broad, there are few analytical results on the statistical properties of these techniques when applied to heteroscedastic time series. Furthermore, there are quite a few papers where the bootstrap procedures used are not adequate. [ABSTRACT FROM AUTHOR]

In this paper, we perform molecular dynamics (MD) simulations to study the random packing of spheres with different particle size distributions. In particular, we deal with non-Gaussian distributions by means of the Lévy distributions. The initial positions as well as the radii of five thousand non-overlapping particles are assigned inside a confining rectangular box. After that, the system is allowed to settle under gravity towards the bottom of the box. Both the translational and rotational movements of each particle are considered in the simulations. In order to deal with interacting particles, we take into account both the contact and long-range cohesive forces. The normal viscoelastic force is calculated according to the nonlinear Hertz model, whereas the tangential force is calculated through an accurate nonlinear-spring model. Assuming a molecular approach, we account for the long-range cohesive forces using a Lennard-Jones (LJ)-like potential. The packing processes are studied assuming different long-range interaction strengths. • Packing dynamics is sensitive to both the distribution type and long-range forces. • The packing density gradually decays as the ε values increase. • The mean coordination number gradually decays as the ε values increase. • The Lévy type II distribution yields the highest packing densities. [ABSTRACT FROM AUTHOR]

Uncertainty-aware design and management of urban water systems lies on the generation of synthetic series that should precisely reproduce the distributional and dependence properties of residential water demand process (i.e., significant deviation from Gaussianity, intermittent behaviour, high spatial and temporal variability and a variety of dependence structures) at various temporal and spatial scales of operational interest. This is of high importance since these properties govern the dynamics of the overall system, while prominent simulation methods, such as pulse-based schemes, address partially this issue by preserving part of the marginal behaviour of the process (e.g., low-order statistics) or neglecting the significant aspect of temporal dependence. In this work, we present a single stochastic modelling strategy, applicable at any fine time scale to explicitly preserve both the distributional and dependence properties of the process. The strategy builds upon the Nataf's joint distribution model and particularly on the quantile mapping of an auxiliary Gaussian process, generated by a suitable linear stochastic model, to establish processes with the target marginal distribution and correlation structure. The three real-world case studies examined, reveal the efficiency (suitability) of the simulation strategy in terms of reproducing the variety of marginal and dependence properties encountered in water demand records from 1-min up to 1-h. [ABSTRACT FROM AUTHOR]