Double Exponential Distribution Research Articles

A proposal and simulation analysis for a novel architecture of gate-all-around polycrystalline silicon nanowire field effect transistor

A proposal for a novel gate-all-around (GAA) polycrystalline silicon nanowire (poly-SiNW) field effect transistor (FET) is presented and discussed in this paper. The device architecture is based on the realization of poly-SiNW in a V-shaped cavity obtained by tetra methyl ammonium hydroxide (TMAH) etch of monocrystalline silicon (100). The device’s behavior is simulated using Silvaco commercial software, including the density of states (DOS) model described by the double exponential distribution of acceptor trap density within the gap. The electric field, potential, and free electron concentration are analyzed in different nanowire regions to investigate the device's performance. The results show good performance despite the high density of deep states in poly-SiNW. This can be explained by the strong electric field caused by the corner effect in the nanowire, which favors the ionization of the acceptor traps and increases the free electron concentration.

On moments of truncated multivariate normal/independent distributions

Multivariate normal/independent (MNI) distributions contain many renowned heavy-tailed distributions such as the multivariate t, multivariate slash, multivariate contaminated normal, multivariate variance-gamma, and multivariate double exponential distributions. A frequent problem encountered in statistical analysis is the occurrence of truncated observations and non-normality such that theoretical moments are required for the estimation of the truncated multivariate normal/independent (TMNI) distributions. This paper is dedicated to deriving explicit expressions for the moments of the TMNI distributions with supports confined within a hyper-rectangle. A Monte Carlo experiment is undertaken to validate to the correctness of the proposed formulae for five selected members of the TMNI distributions. R scripts and data to reproduce the results are available in the GitHub repository.

The spike-and-slab lasso and scalable algorithm to accommodate multinomial outcomes in variable selection problems

Spike-and-slab prior distributions are used to impose variable selection in Bayesian regression-style problems with many possible predictors. These priors are a mixture of two zero-centered distributions with differing variances, resulting in different shrinkage levels on parameter estimates based on whether they are relevant to the outcome. The spike-and-slab lasso assigns mixtures of double exponential distributions as priors for the parameters. This framework was initially developed for linear models, later developed for generalized linear models, and shown to perform well in scenarios requiring sparse solutions. Standard formulations of generalized linear models cannot immediately accommodate categorical outcomes with > 2 categories, i.e. multinomial outcomes, and require modifications to model specification and parameter estimation. Such modifications are relatively straightforward in a Classical setting but require additional theoretical and computational considerations in Bayesian settings, which can depend on the choice of prior distributions for the parameters of interest. While previous developments of the spike-and-slab lasso focused on continuous, count, and/or binary outcomes, we generalize the spike-and-slab lasso to accommodate multinomial outcomes, developing both the theoretical basis for the model and an expectation-maximization algorithm to fit the model. To our knowledge, this is the first generalization of the spike-and-slab lasso to allow for multinomial outcomes.

Double-Exponential-X Family of Distributions: Properties and Applications

A new family of distribution named Double-Exponential-X family is proposed. The proposed family is generated from the double exponential distribution. The forms of the probability densities and hazard functions of two distinct subfamilies of the proposed family are examined and reported. Generalproperties such as moment, survival, order statistics, probability weighted moments and quartile functions of the models are investigated. A sub family of the developed family of double –Exponential-X family of the distribution known as double-Exponential-Pareto distribution was used to fit a real life data on the use of antiretroviral drugs. Molecular simulation of efficacy of antiretroviral drugs is conducted to evaluate the performance of the model. The models were tested using some models diagnostic tests and it was revealed that the proposed model was better than the ones proposed before it from the same family and also, stochastic dominance method was used to affirm the best antiretroviral drugs used in the study.

Design Hydrographs in Small Watersheds from General Unit Hydrograph Model and NRCS-NOAA Rainfall Distributions

It is time to shift our paradigm of small watershed design from a graphic (or tabular) to a theoretical method, because (1) the recent general unit hydrograph (UH) model can convert a design hyetograph to a design hydrograph simply, accurately, and theoretically; (2) the Natural Resources Conservation Service (NRCS) has recommended that the National Oceanic and Atmospheric Administration (NOAA) Atlas 14 rainfall data of depths and distributions at a specific site, which is often called the NRCS-NOAA rainfall distributions, should be used for small watershed design if runoff data are unavailable; and (3) in this paper, we have presented a design procedure that formulates design hydrographs from the NRCS-NOAA Atlas 14 rainfall distributions and the general UH model automatically, using the MATLAB convolution function. A literature review indicated that the current practice for design hydrographs in small watersheds from hyetographs is laborious because both hyetographs and UHs are discrete. By contrast, the theoretical general UH model can significantly simplify this process. In this research, we first found analytic design hydrographs from rectangular and triangular hyetographs, which were next used to validate the MATLAB convolution method. We then proposed a double exponential rainfall distribution for both asymmetric and symmetric hyetographs. After that, we modified the symmetric exponential distribution model to describe NRCS-NOAA Atlas 14 data for site-specific hyetographs, which are finally convolved with the general UH model for site-specific design hydrographs, using the MATLAB convolution function. It is noteworthy that the proposed method extends the classic rational method from the peak discharge to the whole hydrograph; and it is valid for both continuous and discrete hyetographs. Hence, it provides a powerful tool in urban development, agriculture land use, roadway planning, and airport construction; it can also be used to evaluate an existing drainage system under various meteorologic–hydrologic conditions. Finally, we expect that this research will shift our current design practice and university UH teaching from an empirical to a theoretical paradigm in the near future.

Luminescence principle and characteristics of imaging plate

The imaging plate (IP) is a reusable detector for detecting radiation particles in a complex electromagnetic field environment, and it is widely used as a detection medium in laser-accelerated particle beam diagnostic equipment. Therefore, it is necessary to study the performance characteristics and physical mechanism of IP. An electron source with known activity is used to explore the performance characteristics of IP. A <sup>90</sup>Sr/<sup>90</sup>Y electron source is used to measure the time attenuation curve, calibrate the absolute sensitivity, and study the law of multiple scanning of BAS-SR and BAS-TR. In the case of a longer irradiation, the fading cannot be neglected, and the attenuation curves are modified. The time attenuation characteristics indicate that the IP should be cooled after irradiation, and the scanning should be carried out in the slow decay process to reduce the influence of the reading error in the decay process. The absolute sensitivity of BAS-SR and BAS-TR to <sup>90</sup>Sr/<sup>90</sup>Y source are (0.033±0.002) PSL/<i>e</i> and (0.018±0.0038) PSL/<i>e</i> (photostimulated light, PSL), respectively, which are consistent with the results of most absolute sensitivity. The absolute sensitivity is closely related to the type of IP, scanning equipment, and experimental environment. In addition, the energy spectrum integral effect of the broad spectrum <i>β</i> source has a significant influence on the absolute sensitivity. This method is only suitable for the rough evaluation of the sensitivity characteristic parameters of the IP. Multiple scanning approximately satisfies the double exponential function distribution, which is consistent with the physical model. The characteristics of IP are determined by its storage principle. The fluorescence layer of IP is composed of typical electron trapping materials <i>M</i>F<i>X</i> (<i>M</i> = Ca, Sr, Ba; <i>X</i> = C1, Br, I) alkaline earth metal fluorhalide BaFBr. When the IP is irradiated, a large number of free electron-hole pairs are excited by the deposited energy in the material, and the free electrons will be captured by the electron trap, so the fluorescence layer of the IP records the radiation particles’ information through the energy deposited. In this paper, we study three kinds of models. Based on the models, a photo-stimulated luminescence model is proposed to describe the electron transfer process. The photo-stimulated luminescence model describes the physical mechanism of energy deposition, information storage, and information scanning of radiation particles. The relationship between the physical mechanism and characteristics is explained effectively by combining the microscopic mathematical model with the macroscopic physical phenomenon. It provides a specific data basis for the subsequent application of IPs in laser plasma diagnostic experiments.

A new Bayesian lasso and ridge regression with a practically meaningful parameterization and a simple weakly informative prior

Bayesian lasso mimics the regular lasso penalty by placing a double‐exponential prior on the regression coefficients. It automatically provides integrated interval estimates that the regular lasso does not do. Bayesian lasso has found many applications from genetics and genomics to text categorization to traffic safety. The difficulty in specifying a sensible prior for the rate of the double exponential distribution for a particular application, however, is a significant barrier for the wider use of this methodology. This paper proposes a new Bayesian lasso formulation. Instead of using the rate of the double exponential distribution, the new formulation uses a standardized total effect size as the parameter that determines the level of shrinkage with several significant advantages. First, an informative prior is more effectively constructed and understood for this practically meaningful parameter. Second, a weakly informative prior for this new parameter is derived, which allows a practicing statistician to carry out the analysis in an automated way when an informative prior is difficult to elucidate. Third, it is more flexible in modelling prior distributions. A parallel new formulation for Bayesian ridge regression is also provided. A simple and efficient Stan implementation is supplied that can be readily used.

Сравнительный анализ устойчивости различных методов оценивания параметров билинейной авторегрессионной модели

The purpose of this work is to compare various methods in evaluating parameters of a bilinear autoregressive model. Least squares estimate, least absolute deviations estimate and estimate based on the Huber function were used as the parameter estimates. Computer simulation was introduced to study the indicated estimates precision depending on probability distribution of the bilinear autoregressive model upgrading process. Probable distribution of the upgrading process was simulated by normal and uniform distributions, Student distribution with various degrees of freedom, Laplace distribution (double exponential distribution), and Tukey distribution known as the polluted normal distribution. Their mean square error served as the evaluation precision measure. Results of the conducted computational experiment showed that precision of three methods used in evaluating parameters of the bilinear autoregressive series significantly depended on probability distribution of the model upgrading process. In particular, it concerns the number of degrees of freedom of the Student distribution, as well as the Tukey distribution pollution share and amount. If the upgrading process possesses normal and uniform distributions, Student’s distribution with sufficiently high number of degrees of freedom, the least squares method works more efficiently. Estimate based on the Huber function and the least absolute deviations estimate are becoming more efficient compared to the least squares estimation for the Laplace distribution, with a decrease in the number of degrees of freedom --- for the Student distribution, and with an increase in the pollution share and amount --- for the Tukey distribution

Robust Inference and Modeling of Mean and Dispersion for Generalized Linear Models

Generalized Linear Models (GLMs) are a popular class of regression models when the responses follow a distribution in the exponential family. In real data the variability often deviates from the relation imposed by the exponential family distribution, which results in over- or underdispersion. Dispersion effects may even vary in the data. Such datasets do not follow the traditional GLM distributional assumptions, leading to unreliable inference. Therefore, the family of double exponential distributions has been proposed, which models both the mean and the dispersion as a function of covariates in the GLM framework. Since standard maximum likelihood inference is highly susceptible to the possible presence of outliers, we propose the robust double exponential (RDE) estimator. Asymptotic properties and robustness of the RDE estimator are discussed. A generalized robust quasi-deviance measure is introduced which constitutes the basis for a stable robust test. Simulations for binomial and Poisson models show the excellent performance of the RDE estimator and corresponding robust tests. Penalized versions of the RDE estimator are developed for sparse estimation with high-dimensional data and for flexible estimation via generalized additive models (GAMs). Real data applications illustrate the relevance of robust inference for dispersion effects in GLMs and GAMs. Supplementary materials for this article are available online.

A Bayesian Singular Value Decomposition Procedure for Missing Data Imputation

Missing data are common in empirical studies. Multiple imputation is a method to handle missing values by replacing them with plausible values. A common imputation method is multiple imputation with chain equations (MICE). MICE defines a series of conditional distributions to impute missing values. Although MICE is relatively easy to implement, it may not converge to a proper joint distribution. An alternative strategy is to model the variables jointly using the general location model, but this model can become complex when the number of variables increases. Both approaches require integration of prior information when there are more variables than cases. We propose a Bayesian model that is based on the singular value decomposition components of a continuous data matrix to impute missing values. The model assumes that the matrix is of low rank by applying double exponential prior distributions on the singular values. We describe an efficient sampling algorithm to estimate the model’s parameters and impute the missing data. The performance of the model is compared to current imputation methods in simulated and real datasets. Of all the methods considered and in most of the simulated and real datasets, the proposed procedure appears to be the most accurate and precise. Supplementary materials for this article are available online.

An Overview of Composite Standard Elastic-Net Distribution Based on Complex Wavelet Coefficients

Statistical tools have changed significantly in the past decade; when the maximum likelihood method is usually applied, it provides an inaccurate solution due to its unsuitable properties and causes problems in fit. However, the current Ordinary Least Square (OLS) Model is more reliable in specific situations where the estimation is based on the slope only. On the other hand, some methods depend on the slope, and the intercept is recommended. These methods can be described as thresholding rules. Another often preferred method is the posterior mean (PM) technique. This procedure depends on two parts, the first part is the likelihood, and the other is the prior distribution, where the second part plays a significant role in the estimation. In this article, the standard elastic-net distribution is assumed as the prior part, which consists of two parts, the first being the normal distribution and the second being the double exponential distribution. The reason why this model is used is that wavelet tools have different levels of resolution. Thus, this model may provide a more accurate estimation for the wavelet coefficients, which might be estimated using a normal or double exponential distribution. In the past, some properties of elastic-net penalized were introduced and discussed. However, more properties are introduced for this distribution. In addition, two models based on the elastic-net method are demonstrated, involving the point mass prior. The first model combines normal as likelihood, and elastic-net distributions as prior, while the other combines the double exponential distribution as likelihood with the elastic-net distribution as prior. Moreover, the level-dependent components are estimated at each resolutions. A simulated investigation is studied using the Markov Chain Monte Carlo (MCMC) tool to estimate the underlying features, where real data are involved and modelled using the proposed methods. A stationary wavelet basis is also applied. As a result, the proposed procedure reduces noise levels which may be helpful since noise levels often corrupt real data, usually a significant cause of most numerical estimation problems.

The Analysis of WJ Distribution as an Extended Gaussian Function: Case Study

The double exponential WJ distribution has been shown to competently describe extreme events and critical phenomena, while the Gaussian function has celebrated rich applications in many other fields. Here we present the analysis that the WJ distribution may be properly treated as an extended Gaussian function. Based on the Taylor expansion, we propose three methods to formulate the WJ distribution in the form of Gaussian functions, with Method I and Method III being accurate and self-consistent, and elaborate the relationship among the parameters of the functions. Moreover, we derive the parameter scaling formula of the WJ distribution to express a general Gaussian function, with the work illustrated by a classical case of extreme events and critical phenomena and application to topical medical image processing to prove the effectiveness of the WJ distribution rather than the Gaussian function. Our results sturdily advocate that the WJ distribution can elegantly represent a Gaussian function of arbitrary parameters, whereas the latter usually is not able to satisfactorily describe the former except for specific parameter sets. Thus, it is conclusive that the WJ distribution offers applicability in extreme events and critical phenomena as well as processes describable by the Gaussian function, namely, implying plausibly a unifying approach to the pertinent data processing of those quite distinct areas and establishing a link between relevant extreme value theories and Gaussian processes.

Extreme rainless periods in Pannonian Basin

AbstractThis paper analyses extreme meteorological droughts in the territory of the Pannonian Basin in central and southeastern Europe. Droughts are treated from an agricultural perspective as periods of consecutive days with very little or no rainfall at all. By using data from the historical period 1981–2010, time intervals longer than 20 days with less than 3 mm per day during the growing season April–September are examined to determine theoretical and empirical distributions of their number and durations. Related discrete stochastic process of extremes is analysed by the Zelenhasic–Todorovic (ZT) method, successfully applied in hydrology and meteorology (e.g., peak flows, low flows, meteorological droughts, etc.). The method is applied to 52 locations across Pannonia Basin. At each location, the Poisson distribution is determined for the number of droughts, exponential distribution for the duration of droughts, and double exponential distribution for the duration of the (annually) longest droughts. To validate the quality of modelling and the results obtained, standard statistical goodness of fit tests are used. Historical data from the period 1981–2010 indicate that the central and northern part of Hungary and the entire territory of Vojvodina Province in the north of Serbia experienced the longest droughts, on average 55–60 days. In statistical terms, across Pannonia Basin once in 100 years drought may occur with an average duration of 56 days. Theoretically longest 100‐year droughts could be expected in the northern part of Hungary (up to 70 days), the eastern part of Romania (up to 68 days), and Serbia (up to 69 days). The 2‐year droughts are on the average duration of 3 weeks. Generated maps of the longest droughts in the basin may help to reduce agricultural risks due to global warming and other negative impacts of climate change.

Propagation Characteristics of Obliquely Incident Terahertz Waves in High-Temperature Magnetized Plasma

Propagation characteristics of obliquely incident terahertz waves in high-temperature magnetized plasma are studied by the scattering matrix method (SMM) and Wentzel–Kramers–Brillouin (WKB) method. Three cases of electron density distribution (uniform, double exponential, and Epstein distributions) are considered. Numerical simulation exhibits that the SMM can give out the nearly same results with the WKB method, which indicates that these two methods work very well for solving this problem. Through the analysis of the incident angle, we found that as the incident angle increases, it is not conducive to the transmission of left-handed circularly polarized (LCP) waves and right-handed circularly polarized (RCP) waves. When the incident angle increases to a certain value, the phenomenon of “total reflection” will appear. We also systematically calculated the influence of physical parameters such as electron density, collision frequency, plasma thickness, magnetic field strength, and electron temperature on the transmission characteristics. These theoretical results are helpful to alleviate “blackout” problem and improve communication quality.

A limit theorem for the last exit time over a moving nonlinear boundary for a Gaussian process

We prove a limit theorem on the convergence of the distributions of the scaled last exit time over a slowly moving nonlinear boundary for a class of Gaussian stationary processes. The limit is a double exponential (Gumbel) distribution.

CALCULATION OF CLIMATE LOADS DESIGN VALUES ACCORDING TO THE PROBABILITY MODEL OF ANNUAL MAXIMUM SERIES

The aim of this work is to improve a method for determining the characteristic values of climatic loads according to a probabilistic model of the annual maxima sequence, by choosing a rational type of generalized extreme value distribution law. An analysis is provided regarding the suitability of using four types of distributions for describing a data collection of maximum values of climatic loads. Using example data from the meteorological stations of Ukraine, it is found that for coefficients of variation smaller than 0.85–1.0, it is advisable to use the double exponential Gumbel distribution (generalized extreme value distribution type-I), and at higher values of the coefficient of variation, it is advisable to use the Weibull distribution (generalized extreme value distribution type-III). Recommendations are provided for considering the accuracy in the estimations of the characteristic values of loads according to the probabilistic model for the annual maximum value series.

A New Efficient Redescending M-Estimator for Robust Fitting of Linear Regression Models in the Presence of Outliers

Robust regression is an important iterative procedure that seeks analyzing data sets that are contaminated with outliers and unusual observations and reducing their impact over regression coefficients. Robust estimation methods have been introduced to deal with the problem of outliers and provide efficient and stable estimates in their presence. Various robust estimators have been developed in the literature to restrict the unbounded influence of the outliers or leverage points on the model estimates. Here, a new redescending M-estimator is proposed using a novel objective function with the prime focus on getting highly robust and efficient estimates that give promising results. It is evident from the results that, for normal and clean data, the proposed estimator is almost as efficient as ordinary least square method and, however, becomes highly resistant to outliers when it is used for contaminated datasets. The simulation study is being carried out to assess the performance of the proposed redescending M-estimator over different data generation scenarios including normal, t-distribution, and double exponential distributions with different levels of outliers’ contamination, and the results are compared with the existing redescending M-estimators, e.g., Huber, Tukey Biweight, Hampel, and Andrew-Sign function. The performance of the proposed estimators was also checked using real-life data applications of the estimators and found that the proposed estimators give promising results as compared to the existing estimators.

Stochastic Analysis of Rumor Spreading with Multiple Pull Operations

We propose and analyze a new asynchronous rumor spreading protocol to deliver a rumor to all the nodes of a large-scale distributed network. This spreading protocol relies on what we call a k-pull operation, with \(k \ge 2\). Specifically a k-pull operation consists, for an uninformed node s, in contacting \(k-1\) other nodes at random in the network, and if at least one of them knows the rumor, then node s learns it. We perform a thorough study of the total number \(T_{k,n}\) of k-pull operations needed for all the n nodes to learn the rumor. We compute the expected value and the variance of \(T_{k,n}\), together with their limiting values when n tends to infinity. We also analyze the limiting distribution of \((T_{k,n} - {E}(T_{k,n}))/n\) and prove that it has a double exponential distribution when n tends to infinity. Finally, we show that when \(k > 2\), our new protocol requires less operations than the traditional 2-push-pull and 2-push protocols by using stochastic dominance arguments. All these results generalize the standard case \(k=2\).

Mutation Strategy Based on Step Size and Survival Rate for Evolutionary Programming

Evolutionary programming (EP) uses a mutation as a unique operator. Gaussian, Cauchy, Lévy, and double exponential probability distributions and single-point mutation were nominated as mutation operators. Many mutation strategies have been proposed over the last two decades. The most recent EP variant was proposed using a step-size-based self-adaptive mutation operator. In SSEP, the mutation type with its parameters is selected based on the step size, which differs from generation to generation. Several principles for choosing proper parameters have been proposed; however, SSEP still has limitations and does not display outstanding performance on some benchmark functions. In this work, we proposed a novel mutation strategy based on both the “step size” and “survival rate” for EP (SSMSEP). SSMSEP-1 and SSMSEP-2 are two variants of SSMSEP, which use “survival rate” or “step size” separately. Our proposed method can select appropriate mutation operators and update parameters for mutation operators according to diverse landscapes during the evolutionary process. Compared with SSMSEP-1, SSMSEP-2, SSEP, and other EP variants, the SSMSEP demonstrates its robustness and stable performance on most benchmark functions tested.

The Influence of Dusty Size Distribution Model on Propagation of Electromagnetic Waves in Inhomogeneous Plasma Sheath

In this paper, a linear distribution model, a double exponential distribution model and a hyperbolic number distribution model are developed, and the effect of dust particle size distribution on its attenuation coefficient is considered. On this basis, the transmission characteristics of electromagnetic waves in dusty plasma under different electron density distribution models are investigated. The attenuation coefficients of electromagnetic waves are derived in detail using analytical methods, and the effects of electromagnetic wave frequency, particle collision frequency and dust particle density on the transmission characteristics of electromagnetic waves are discussed. The results show that the choice of terahertz wave as the carrier wave and the appropriate change of particle collision frequency can improve the attenuation of electromagnetic waves. In summary, the relevant research can provide some theoretical references for propagation science.