Power Laws and Skew Distributions

Power-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.

The Alpha-Beta-Gamma Skew Normal Distribution and Its Application

In this paper, a new class of skew multimodal distributions with more flexible than alpha skew normal distribution and alpha-beta skew normal distribution is proposed, which makes some important distributions become its special cases. The statistical properties of the new distribution are studied in detail, its moment generating function, skewness coefficient, kurtosis coefficient, Fisher information matrix, maximum likelihood estimators are derived. Moreover, a random simulation study is carried out for test the performance of the estimators, the simulation results show that with the increase of sample size, the mean value of maximum likelihood estimators tends to the true value. The new distribution family provides a better fit compared with other known skew distributions through the analysis of a real data set.

Skew t Distribution-Based Nonlinear Filter with Asymmetric Measurement Noise Using Variational Bayesian Inference

This paper is focused on the state estimation problem for nonlinear systems with unknown statistics of measurement noise.Based on the cubature Kalman filter,we propose a new nonlinear filtering algorithm that employs a skew t distribution to characterize the asymmetry of the measurement noise.The system states and the statistics of skew t noise distribution,including the shape matrix,the scale matrix,and the degree of freedom(DOF)are estimated jointly by employing variational Bayesian(VB)inference.The proposed method is validated in a target tracking example.Results of the simulation indicate that the proposed nonlinear filter can perform satisfactorily in the presence of unknown statistics of measurement noise and outperform than the existing state-of-the-art nonlinear filters.

Variable Selection for Robust Mixture Regression Model with Skew Scale Mixtures of Normal Distributions

In this paper, we propose a robust mixture regression model based on the skew scale mixtures of normal distributions (RMR-SSMN) which can accommodate asymmetric, heavy-tailed and contaminated data better. For the variable selection problem, the penalized likelihood approach with a new combined penalty function which balances the SCAD and l2 penalty is proposed. The adjusted EM algorithm is presented to get parameter estimates of RMR-SSMN models at a faster convergence rate. As simulations show, our mixture models are more robust than general FMR models and the new combined penalty function outperforms SCAD for variable selection. Finally, the proposed methodology and algorithm are applied to a real data set and achieve reasonable results.

FG-SMOTE:Fuzzy-based Gaussian synthetic minority oversampling with deep belief networks classifier for skewed class distribution

Purpose-Adequate resources for learning and training the data are an important constraint to develop an efficient classifier with outstanding performance.The data usually follows a biased distribution of classes that reflects an unequal distribution of classes within a dataset.This issue is known as the imbalance problem,which is one of the most common issues occurring in real-time applications.Learning of imbalanced datasets is a ubiquitous challenge in the field of data mining.Imbalanced data degrades the performance of the classifier by producing inaccurate results.Design/methodology/approach-In the proposed work,a novel fuzzy-based Gaussian synthetic minority oversampling(FG-SMOTE)algorithm is proposed to process the imbalanced data.The mechanism of the Gaussian SMOTE technique is based on finding the nearest neighbour concept to balance the ratio between minority and majority class datasets.The ratio of the datasets belonging to the minority and majority class is balanced using a fuzzy-based Levenshtein distance measure technique.Findings-The performance and the accuracy of the proposed algorithm is evaluated using the deep belief networks classifier and the results showed the efficiency of the fuzzy-based Gaussian SMOTE technique achieved an AUC:93.7%.F1 Score Prediction:94.2%,Geometric Mean Score:93.6%predicted from confusion matrix.Research limitations/implications-The proposed research still retains some of the challenges that need to be focused such as application FG-SMOTE to multiclass imbalanced dataset and to evaluate dataset imbalance problem in a distributed environment.Originality/value-The proposed algorithm fundamentally solves the data imbalance issues and challenges involved in handling the imbalanced data.FG-SMOTE has aided in balancing minority and majority class datasets.

Third Order Adjoint Sensitivity and Uncertainty Analysis of an OECD/NEA Reactor Physics Benchmark: III. Response Moments

The (180)3 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cross sections have been computed in accompanying works [1] [2]. This work quantifies the contributions of these (180)3 third-order mixed sensitivities to the PERP benchmark’s leakage response distribution moments (expected value, variance and skewness) and compares these contributions to those stemming from the corresponding first- and second-order sensitivities of the PERP benchmark’s leakage response with respect to the total cross sections. The numerical results obtained in this work reveal that the importance of the 3rd-order sensitivities can surpass the importance of the 1st- and 2nd-order sensitivities when the parameters’ uncertainties increase. In particular, for a uniform standard deviation of 10% of the microscopic total cross sections, the 3rd-order sensitivities contribute 80% to the response variance, whereas the contribution stemming from the 1st- and 2nd-order sensitivities amount only to 2% and 18%, respectively. Consequently, neglecting the 3rd-order sensitivities could cause a very large non-conservative error by under-reporting the response variance by a factor of 506%. The results obtained in this work also indicate that the effects of the 3rd-order sensitivities are to reduce the response’s skewness in parameter space, rendering the distribution of the leakage response more symmetric about its expected value. The results obtained in this work are the first such results ever published in reactor physics. Since correlations among the group-averaged microscopic total cross sections are not available, only the effects of typical standard deviations for these cross sections could be considered. Due to this lack of correlations among the cross sections, the effects of the mixed 3rd-order sensitivities could not be quantified exactly at this time. These effects could be quantified only when correlations among the group-averaged microscopic total cross sections would be obtained experimentally by the nuclear physics community.

Third-Order Adjoint Sensitivity Analysis of an OECD/NEA Reactor Physics Benchmark: I. Mathematical Framework

This work extends to third-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The PERP benchmark comprises 21,976 imprecisely known (uncertain) model parameters. Previous works have used the adjoint sensitivity analysis methodology to compute exactly and efficiently all of the 21,976 first-order and (21,976)2 second-order sensitivities of the PERP benchmark’s leakage response to all of the benchmark’s uncertain parameters, showing that the largest and most consequential 1st- and 2nd-order response sensitivities are with respect to the total microscopic cross sections. These results have motivated extending the previous adjoint-based derivations to third-order, leading to the derivation, in this work, of the exact mathematical expressions of the (180)3 third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections. The formulas derived in this work are valid not only for the PERP benchmark but can also be used for computing the 3rd-order sensitivities of the leakage response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of these (180)3 third-order sensitivities (which turned out to be very large and consequential) and use them for a third-order uncertainty analysis of the PERP benchmark’s leakage response.

Mathematical Insight into Moderate Inversion Gate Delay Variability for Ultradeep Submicron Digital Circuit Design

Voltage scaling has been extensively used in industry for decades to reduce power consumption.In recent years,exploring digital circuit operation in moderate inversion has created an interest among researchers due to its immense capability to provide a perfect tradeoff between high performance and low energy operation.But circuits operating in moderate inversion are susceptible to process variations and variability.To compute variability,statistical parameters such as the probability density function(PDF)and cumulative distribution function(CDF)are required.This paper presents an analytical model framework for delay calculations utilizing log skew normal distribution for ultradeep submicron technology nodes up to 22 nm.The CDF of the proposed model is utilized to calculate minimum and maximum delays with 3σ-accuracy providing better accuracy than the conventional methods.The obtained results are also compared with Monte Carlo simulations with errors lying within the acceptable range of 2%-4%.

GARCH-Type modeling of stock market returns for the pre-crisis countries

Empirical studies have shown that a large number of financial asset returns exhibit fat tails （leptokurtosis） and are often characterized by volatility clustering and asymmetry. This paper considers the ability of the GARCH-Type （Generalized Autoregressive Conditional Heteroskedasticity） models to capture the stylized features of volatility in national stock market returns for three countries （Portugal, Spain and Greece）. The results of this paper suggest that in the presence of asymmetric responses to innovations in the market, the ARMA （1,1）-GJRGARCH（1,1） skewed Student-t model which accommodates both the skewness and the kurtosis of financial time series is preferred.

Inferences in Linear Mixed Models with Skew-normal Random Effects

For the linear mixed model with skew-normal random effects, this paper gives the density function, moment generating function and independence conditions. The noncentral skew chi-square distribution is defined and its density function is shown. The necessary and sufficient conditions under which a quadratic form is distributed as noncentral skew chi-square distribution are obtained. Also, a version of Cochran＇s theorem is given~ which modifies the result of Wang et al. （2009） and is used to set up exact tests for fixed effects and variance components of the proposed model. For illustration, our main results are applied to a real data problem.

Uncertainty modeling of wind power frequency regulation potential considering distributed characteristics of forecast errors

Large-scale integration of wind power generation decreases the equivalent inertia of a power system, and thus makes frequency stability control challenging. However, given the irregular, nonlinear, and non-stationary characteristics of wind power, significant challenges arise in making wind power generation participate in system frequency regulation. Hence, it is important to explore wind power frequency regulation potential and its uncertainty. This paper proposes an innovative uncertainty modeling method based on mixed skew generalized error distribution for wind power frequency regulation potential. The mapping relationship between wind speed and the associated frequency regulation potential is established, and key parameters of the wind turbine model are identified to predict the wind power frequency regulation potential. Furthermore, the prediction error distribution of the frequency regulation potential is obtained from the mixed skew model. Because of the characteristics of error partition, the error distribution model and predicted values at different wind speed sections are summarized to generate the uncertainty interval of wind power frequency regulation potential. Numerical experiments demonstrate that the proposed model outperforms other state-of-the-art contrastive models in terms of the refined degree of fitting error distribution characteristics. The proposed model only requires the wind speed prediction sequence to accurately model the uncertainty interval. This should be of great significance for rationally optimizing system frequency regulation resources and reducing redundant backup.

Prediction and datamining of burned areas of forest fires:Optimized data matching and mining algorithm provides valuable insight

An optimized data-matching machine learning algorithm is developed to provide high-prediction accuracy of total burned areas for specific wildfire incidents.It is applied to a well-studied forest-fire dataset from Portugal Montesinho Natural Park considering 13 input variables.The total burned area distribution of the 517 burn events in that dataset is highly positively skewed.The model is transparent and avoids regressions and hidden layers.This increases its detailed datamining capabilities.It matches the highest burned-area prediction accuracy achieved for this datasetwith a wide range of traditionalmachine learning algorithms.The two-stage prediction process provides informative feature selection that establishes the relative influences of the input variables on burned-area predictions.Optimizing with mean absolute error(MAE)and root mean square error(RMSE)as separate objective functions provides complementary information with which to data mine each total burnedarea incident.Such insight offers potential agricultural,ecological,environmental and forestry benefits by improving the understanding of the key influences associated with each burn event.Data mining the differential trends of cumulative absolute error and squared error also provides detailed insight with which to determine the suitability of each optimized solution to accurately predict burned-areas events of specific types.Such prediction accuracy and insight leads to confidence in how each prediction is derived.It provides knowledge to make appropriate responses and mitigate specific burn incidents,as they occur.Such informed responses should lead to short-term and long-term multi-faceted benefits by helping to prevent certain types of burn incidents being repeated or spread.

Stochastic simulation of fluid flow in porous media by the complex variable expression method

A stochastic simulation of fluid flow in porous media using a complex variable expression method （SFCM） is presented in this paper. Hydraulic conductivity is considered as a random variable and is then expressed in complex variable form, the real part of which is a deterministic value and the imaginary part is a variable value. The stochastic seepage flow is simulated with the SFCM and is compared with the results calculated with the Monte Carlo stochastic finite element method. In using the Monte Carlo method to simulate the stochastic seepage flow field, the hydraulic conductivity is assumed in three different probability distributions using random sampling method. The obtained seepage flow field is examined through skewness analysis, and the skewed distribution probability density function is given. The head mode value and the head comprehensive standard deviation are used to represent the statistics of calculation results obtained by the Monte Carlo method. The stochastic seepage flow field simulated by the SFCM is confirmed to be similar to that given by the Monte Carlo method from numerical aspects. The range of coefficient of variation of hydraulic conductivity in SFCM is larger than used previously in stochastic seepage flow field simulations, and the computation time is short. The results proved that the SFCM is a convenient calculating method for solving the complex problems.