Search

This manuscript deals with a novel, nonlinear, and non-stationary stochastic model with symmetric, Laplacian distributed innovations. The obtained model, named Laplacian Split-BREAK (LSB) process, is intended for dynamic analysis of time series with pronounced and permanent fluctuations. By using the method of characteristic functions (CFs), the basic stochastic properties of the LSB process are proven, with a special emphasis on its asymptotic behaviour. The different procedures for estimating its parameters are also given, along with numerical simulations of the obtained estimators. Finally, it has been shown that the LSB process, as an adequate stochastic model, can be applied in the analysis of dynamics in the world market of crude oil and natural gas.

The study of probability distribution has expanded the field of statistical modelling of real life data. It has also provided solution to the problems of skewed data which often violate the normality. This research work introduces a new T Half-Lapalace{Exponential} family with a novel Half-Laplace distribution as baseline distribution with specific interest in three-parameter lifetime model called the Weibull-Half-Lapalace{Exponential} (W-HLa{E}) distribution. The W-HLa{E} model is capable of modeling various shapes of aging events. The W-HLa{E} distribution is derived by combining Half-Laplace and Weibull distribution using the quartile function of Exponential distribution. Some of its statistical properties such as the mean, mode, quantile function, median, variance, standard deviation, skewness, and kurtosis are derived. Other statistical properties such as survival function, hazard rate, moments, asymptotic limit, order statistics, and entropy which is the measure of uncertainty of a random variable are derived and studied. The parameter estimation method adopted in this study is the maximum likelihood method. The graphs of W-HLa{E} at different values of shape and scale parameters show that the distribution is unimodal hence the mode is given as 𝑚𝑜𝑑𝑒 = 𝜃 + ((k-1)/k)¹/ᵏ and it is positively skewed with a steep peak. A simulation study is carried on the new proposed distribution using maximum likelihood estimation. The simulation also supported the theoretical expression of the statistical properties of the proposed distribution such as the location parameter does not affect the variance, skewness, and kurtosis of the new distribution. The importance and the flexibility of the proposed distribution in modeling some real life data sets is demonstrated in the research. The results of the study shows that the proposed W-HLa{E} distribution perform better than other disributions in the literature.

Although massive pruning methods are emerging for achieving structural sparsity in convolutional neural networks (CNN), most of them target structures such as ResNet. Meanwhile, previous works take more interest in pruning filters inside a residual block and keep the shortcut connection intact, leading to an imbalanced network structure. In this paper, we focus on the penalty-based method to prune already compact networks. In contrast to the broadly used L1 constraint, which shrinks the parameters uniformly, we propose a novel penalty term that is similar in shape to an upside-down Laplace distribution. The penalty allows us to impose more pressure on potential weak channels but protects others during training to avoid damaging crucial channels, especially for compact architectures. We also design a candidate selection strategy to cooperate with the penalty-based training procedure. Besides, we address the residual block pruning problem by a scaling factor elimination skill, which is often ignored in other research. Our method reduces 50% parameters of MobileNet v1/v2 with a tolerable accuracy degradation. We further conduct pruning on MobileNetv1-SSDLite to compress parameters by 60%, manifesting the ability to generalize to different visual tasks. The experiment results demonstrate that our method outperforms pruning frameworks based on channel importance without a complicated tuning for hyper-parameters like search-based methods.

Deconvolution technique can be utilized in the forward-looking radar (FLR). However, the forward-looking imaging performance degenerates greatly due to the effect of high-speed movement of the platform. In this article, an efficient Bayesian forward-looking superresolution imaging algorithm based on Doppler deconvolution in expanded beam space is proposed. First, the Doppler phase information caused by the high-speed platform is fully exploited and the Doppler matrix is integrated with the antenna pattern. The Doppler convolution model of the echo signal for forward-looking is derived in this article. Then, the Doppler phase information is adopted to perform the Doppler deconvolution. Moreover, an expanded beam space is constructed to enhance the sparsity of the imaging scene. The complex Gaussian distribution and the Laplace distribution have been used to model the distribution characteristics of noise and targets in the imaging scene, respectively. Finally, based on the Bayesian framework, the forward-looking imaging problem is converted into the convex optimization problem. The performance assessment based on simulated and experimental data, also in comparison to the conventional real beam, truncated singular value decomposition (TSVD), iterative adaptive approach (IAA) methods, has demonstrated the effectiveness of our proposed algorithm under high-speed platform scenarios.

The article studies the supply chain of suppliers and manufacturers, considering the overall benefits of the supply chain, the measurement sampling plan is the small batch sampling plan with the smallest amount of sampling and the strongest discriminative ability. If the quality characteristic data is a measurement value, and the inspection workload is large and the inspection cost is high, it is recommended to adopt the measurement sampling plan based on the Laplace distribution. On the premise of ensuring quality, try to reduce the number of inspected samples as much as possible to reduce the workload and cost of inspection.

The continuous iteration of an exponential-type function allows to describe a whole range of growths between logarithmical and exponential. This principle has been applied to a class of lifetime di...

This paper presents a robust method for dealing with switching regression problems. Regression models with switch-points are broadly employed in diverse areas. Many traditional methods for switching regressions can falter in the presence of outliers or heavy-tailed distributions because of the modeling assumptions of Gaussian errors. The outlier corruption of datasets is often unavoidable. When misapplied, the Gaussian assumption can lead to incorrect inference making. The Laplace distribution is known as a longer-tailed alternative to the normal distributions and connected with the robust least absolute deviation regression criterion. We propose a robust switching regression model of Laplace distributed errors. To advance robustness, we extend the Laplace switching model to a fuzzy class model and create a robust algorithm named FCL through the fuzzy classification maximum likelihood procedure. The robustness properties and the advance of resistance against high-leverage outliers are discussed. Simulations and sensitivity analyses illustrate the effectiveness and superiority of the proposed algorithm. The experimental results indicate that FCL is much more robust than the EM-based algorithm. Furthermore, the Laplace-based algorithm is more time-saving than the t-based procedure. Diverse real-world applications demonstrate the practicality of the proposed approach.

The paper deals with the analysis of the empirical distribution of returns of selected market indices of developed and developing markets in relation to applications in the field of financial risks. The probability distribution of returns plays a key role for both the theoretical and practical part of financial theory. The assumption of a normal distribution of returns, which is crucial for several financial theories, is rejected in line with our analysis of the daily returns of 30 markets. From the perspective of financial risk assessment, the choice of an appropriate distribution is key to the accuracy of the achieved results. In this paper, we examine the possibility of applying alternative distributions, in order to better capture the observed leptokurtic behavior of the empirical distribution of daily returns as compared to the assumption of normality. We perform the analysis on the daily returns of stock market indices in order to examine the possible differences between the empirical distribution of developed and emerging markets. We investigate the suitability and relative performance of these alternative distributions: the generalized skewed t distribution (sgt), the generalized lambda distribution (gld), the exponential power distribution (GED), the Hansen's skewed t distribution and the Laplace distribution. The best relative performance of fit for market index returns providing the sgt_2 and gld distributions, with gld appearing to be a more prominent adept than with the perspective of relative stability of quality of fit and also quality of risk estimation.

Full-waveform inversion (FWI) is a powerful methodology employed in estimating subsurface physical parameters. FWI is classically formulated as a data-fitting problem based on minimizing the squared $$l_2$$ -norm of the difference between the observed data and modeled data (i.e., the data residuals or errors). The FWI based on $$l_2$$ -norm (hereafter classical FWI) stems from the assumption that the errors follow a Gaussian probability distribution. However, since, in most cases the error is non-Gaussian for non-linear problems and therefore, the classical FWI tends to fail. In this work, we consider the Tsallis q-deformation of the exponential function, which is widely used in the field of statistical physics, to derive an alternative misfit function to mitigate the FWI sensitivity to spurious measurements (outliers). In this regard, we formulated the FWI from a q-generalization of the Laplace probability distribution (or q-Laplace distribution). Application on a typical Brazilian pre-salt velocity model with an acoustic synthetic noisy-data is presented, in which we compare the performance of our proposal against the classical FWI. In addition, we compare also our methodology with the robust misfit function based on $$l_1$$ -norm, which is based on the Laplace distribution. The results show that our proposal outperforms classical FWI, and also the robust FWI based on $$l_1$$ -norm. The results also reveal that our proposal accelerates the data inversion process when the data is polluted by outliers.

We consider density deconvolution with zero-mean Laplace noise in the context of an error component regression model. We adapt the minimax deconvolution methods of Meister (2006) to allow estimation of the unknown noise variance. We propose a semi-uniformly consistent estimator for an ordinary-smooth target density and a modified "variance truncation device” for the unknown noise variance. We provide a simulation study and practical guidance for the choice of smoothness parameters of the ordinary-smooth target density. We apply restricted versions of our estimator to a stochastic frontier model of US banks and to a measurement error model of daily saturated fat intake.

Vibration monitoring has been a reliable source of information for machine fault diagnosis. Several methods are available for bearing fault diagnosis under constant speed condition. A fault diagnosis framework consisting of a novel pre-processing tool, named cumulative distribution sharpness (CDS) profiling is proposed for variable speed conditions. We first provide evidences suggesting that the bearing fault signals follow Laplace distribution. Under the influence of Gaussian noise, however, the sharpness of the distribution decreases. This is helpful in separating the periodic fault and noise regions in the time-domain vibration signal by calculating local CDS values. The proposed CDS profiling (CDSP) is thus obtained by sweeping a window over the vibration signal and estimating the sharpness of cumulative distribution of such windowed signal. For changing noise variance, the monotonous and continuous nature of CDS is ensured to obtain a profile that retains the fault periodicity. A short-time Fourier transform of the CDSP is then calculated, followed by multiple time-frequency curves extraction (MTFCE). Two important fault features - Prominence and Compliance - are proposed in this paper. Finally, a fuzzy inference system is used to obtain diagnosis percentages from the features. Thus, the proposed method can classify the faults into healthy, inner race and outer race faults. The results are then validated on experimental data with variable operating speed. We show that prominence of the fault characteristic frequency improves due to CDSP. The accuracy of the proposed method is found to be better than the benchmark method of MTFCE.

In this brief, we investigate the robust state estimation of nonlinear systems with heavy-tailed noise. Based on the fact that the multivariate Laplace (ML) distribution has heavier tails than Gaussian distribution but is only determined by its mean and covariance, we utilize the ML distribution to model the heavy-tailed measurement noise. Based on the Gaussian mixture form of ML distribution, the system state and the covariance of ML distribution are inferred by variational Bayesian method, and then a closed recursive robust nonlinear Kalman filter is obtained with the nonlinear integrations calculated by numerical integration methods. Simulation results demonstrate that the proposed algorithm is insensitive to its free parameters and can obtain better estimation accuracy than related robust algorithms.

In this article, the Laplace distribution is employed in lieu of the well-known normal distribution for finding better scalar values of risk. Explicit formulas for value-at-risk (VaR) and conditional value-at-risk (CVaR) are studied and used to manage the risk involved in a stock movement by using the GARCH model. Numerical simulations are given for a variety of stocks in equity markets to uphold the findings.

Background: The performance of Mobile Ad-hoc Networks gets severely degraded due to various attacks including the Selfish Behaviour attack. The detection of malicious nodes and avoidance of such nodes for data forwarding is important to enhance the MANET’s performance. Methods: A probabilistic model based on Single-Sided Laplacian distribution for the random ON/OFF switching time of this attack is proposed. The model is used to make appropriate decisions regarding the assignment of trust levels to suspicious nodes. The proposed protocol, based on this trust along with Confidence values of nodes, referred to as OLSRT-C protocol is used to select the optimum path for data forwarding. Simulations are carried out using Network Simulator NS-2.35. Results: The random behavior of the Selfish Behaviour attack is analyzed by considering all the possible random parameters. The random deployment of mobile nodes, number of malicious nodes, number of times the malicious nodes switch and timing instances at which these nodes change their states are considered. From the results, it is observed that the OLSRT-C protocol gives stable performance for Packet Delivery Ratio and Routing Overheads whereas, for OLSR protocol, the Packet Delivery Ratio gradually reduces and Routing Overheads increase, for the percentage of malicious nodes increases from 10% to 50%. For OLSRT-C protocol, Average Energy Consumption per node increases marginally compared to the OLSR protocol. Conclusion: The proposed OLSRT-C protocol successfully mitigates the randomized Selfish Behaviour attack with a marginal increase in the Average Energy Consumption per node. The Protocol Efficacy for OLSRT-C protocol is much higher compared to the OLSR protocol.

As a generative model , probabilistic linear discriminant analysis (PLDA) has achieved good performance in supervised learning tasks. The model incorporates both within-individual and between-individual variation, and remaining unexplained data variation is assumed to follow Gaussian distribution . However, the assumption of Gaussian distribution makes the model sensitive to the presence of noise and outliers in training set. To address this issue, this paper proposes a robust probabilistic linear discriminant analysis model by assuming Laplace prior on the noise term. Instead of solving high-dimensional linear systems, we embed a Kronecker-decomposable component in the new model for tensor data, significantly reducing the size of problems. As the non-conjugacy of Laplace distribution complicates the calculation of the posteriors of latent variables, we express it to a hierarchical architecture using an Inverse Gamma distribution and then adopt variational expectation–maximization (EM) algorithm to learn model parameters. The reconstruction and classification experiments on several public databases show the superiority of the proposed model compared with the state-of-the-art LDA-based algorithms.

HighLights • Explore maximum entropy minimum elaborations of simpler maximum entropy models. • Compare maximum entropy priors with parametric modes fitted to elicited quantiles. • Measure uncertainty and disagreement of forecasters with elicited probabilities. • Include the maximizing profit quantile in the newsvendor?s demand distribution., Graphical abstract, Quantiles are available in various problems for developing probability distributions. In some problems quantiles are elicited from experts and used for fitting parametric models, which induce non-elicited information. In some other problems comparisons are made with a quantile of an assumed model which is noncommittal to the quantile information. The maximum entropy (ME) principle provides models that avoid these issues. However, the information theory literature has been mainly concerned about models based on moment information. This paper explores the ME models that are the minimum elaborations of the uniform and moment-based ME models by quantiles. This property provides diagnostics for the utility of elaboration in terms of the information value of each type of information over the other. The ME model with quantiles and moments is represented as the mixture of truncated distributions on consecutive intervals whose shapes and existence are determined by the moments. Elaborations of several ME distributions by quantiles are presented. The ME model based only on quantiles elicited by the fixed interval method possesses a useful property for pooling information elicited from multiple experts. The elaboration of Laplace distribution is an extension of the information theory connection with minimum risk under symmetric loss functions to the asymmetric linear loss. This extension produces a new Asymmetric Laplace distribution. Application examples compare ME priors with a parametric model fitted to elicited quantiles, illustrate measuring uncertainty and disagreement of economic forecasters based on elicited probabilities, and adjust ME models for a fundamental quantile in an inventory management problem.

Esscher transformed Laplace distribution is a new class of asymmetric heavy tailed distribution. In this article, we generalize the Esscher transformed Laplace distribution using the quadratic rank transmutation map to develop transmuted Esscher transformed Laplace distribution. We derived the probability density function of transmuted Esscher transformed Laplace distribution and its various properties were studied. The maximum likelihood estimation procedure is employed to estimate the parameters of the proposed distribution and an algorithm in R package is developed to carry out the estimation. Simulation studies for various choices of parameter values were performed to validate the algorithm. Finally, we fitted the transmuted Esscher transformed Laplace, Esscher transformed Laplace and Gaussian distributions to microarray gene expression dataset and compared them.

Sparse representation based on over-complete dictionaries is a hot issue in the field of computer vision and machine learning. In probability theory, over-complete dictionary can be learned by non-parametric Bayesian techniques with Beta Process. However, traditional probabilistic dictionary learning method assumes noise follows Gaussian distribution, which can only remove Gaussain noise. In order to remove outlier or complex noise, we propose a dictionary learning method based on non-parametric Bayesian technology by assuming the noise follows Laplacian distribution. Because the non-conjugacy of Laplacian distribution makes the calculation of posteriors of latent variables more complicate, thus we utilize a superposition of an infinite number of Gaussian distributions to substitute for L1 density function. The weights of mixture Gaussian distribution are controlled by an extra hidden variable. Then the Bayesian inference is applied to learn all the key parameters in the proposed probabilistic model, which avoids the processing of parameter setting and fine tuning. In the experiments, we mainly test the performance of different algorithms in removing salt-and-pepper noise and mixture noises. The experimental results show that the PSNRs of our algorithm are higher 2-4 dB at least than other classic algorithms.

Запропоновано спеціалізований програмний калькулятор, який надає можливість генерувати засобами ЕXCEL псевдовипадкові числа, розподілені згідно з розподілом Лапласа, розподілом Коші, розподілом найменшого значення, розподілом найбільшого значення, логістичним розподілом, розподілом Чампернауна, подвійним експоненційним розподілом, експоненційним розподілом, розподілом Ерланга порядку m, нормованим розподілом Ерланга порядку m, узагальненим розподілом Ерланга другого порядку, розподілом Вейбулла, зсуненим розподілом Вейбулла, гіперекспоненційним розподілом другого порядку, розподілом модулю n-вимірного випадкового вектору, розподілом Релея, розподілом Релея-Райса, розподілом Максвела, логарифмічно нормальним розподілом, розподілом Парето, розподілом модулю нормально розподіленої випадкової величини, параболічним розподілом, лівобічним зрізаним нормальним розподілом, правобічним зрізаним нормальним розподілом, двобічним зрізаним нормальним розподілом, розподілом арксинусу, розподілом Симпсона (трикутним розподілом), розподілом Бірнбаума-Сандерса, степеневим розподілом, c2-розподілом Пірсона, c-розподілом Пірсона, t-розподілом Стьюдента, F-розподілом Фішера-Снедекора, Z-розподілом Фішера. Наведено основні відомості про структуру спеціалізованого програмного калькулятора. Вказані законі розподілу включено до переліку рекомендованих Міжнародною Спілкою Електрозв’язку для використання в процесі моделювання розповсюдження радіохвиль (документ МСЭ-R P.1057-5 (12/2017).Запропоновано спеціалізований програмний калькулятор для отримання значень функції нормального розподілу для різних форм її подання. Калькулятор реалізовано в середовищі Excel.

Mixture of Experts (MoE) regression models are widely studied in statistics and machine learning for modeling heterogeneity in data for regression, clustering and classification. Laplace distribution is one of the most important statistical tools to analyze thick and tail data. Laplace Mixture of Linear Experts (LMoLE) regression models are based on the Laplace distribution which is more robust. Similar to modelling variance parameter in a homogeneous population, we propose and study a new novel class of models: heteroscedastic Laplace mixture of experts regression models to analyze the heteroscedastic data coming from a heterogeneous population in this paper. The issues of maximum likelihood estimation are addressed. In particular, Minorization-Maximization (MM) algorithm for estimating the regression parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo simulations. Results from the analysis of two real data sets are presented.

In this paper, we consider a comparison between two estimators of the parameter $$p$$ of the discrete Laplace distribution. A new method of moments estimator (MME) is derived and the asymptotic normality of its distribution is proven by applying the classical Delta method. The new MME is compared with the already known maximum likelihood estimator (MLE). Note that no accuracy properties of the MLE have been investigated before. The accuracy and the asymptotic normality of both estimators are investigated theoretically and using Monte Carlo simulation studies. We show that the MLE possesses better accuracy properties than the MME.

Data collected in modern industrial processes often exhibit complex non-Gaussian and multimodal characteristics. In order to address these problems, a robust mixture probabilistic partial least squares (RMPPLS) model-based soft sensor is developed in this article, where two different kinds of hidden variables are introduced in the formulated model structure. The multivariate Laplace distribution is employed for robust modeling, and mixture form of the probabilistic partial least squares model is adopted for multimodal description. The unknown parameters are estimated in the expectation-maximization (EM) scheme and the corresponding soft sensor is finally constructed. A numerical example and the Tennessee Eastman (TE) process case study are explored to verify the effectiveness of the proposed algorithm.

Significant efforts are constantly involved in finding manners to decrease the number of bits required for quantization of neural network parameters. Although in addition to compression, in neural networks, the application of quantizer models that are robust to changes in the variance of input data is of great importance, to the best of authors knowledge, this topic has not been sufficiently researched so far. For that reason, in this paper we give preference to logarithmic companding scalar quantizer, which has shown the best robustness in high quality quantization of speech signals, modelled similarly as weights in neural networks, by Laplacian distribution. We explore its performance by performing the exact and asymptotic analysis for low resolution scenario with 2-bit quantization, where we draw firm conclusions about the usability of the exact performance analysis and design of our quantizer. Moreover, we provide a manner to increase the robustness of the quantizer we propose by involving additional adaptation of the key parameter. Theoretical and experimental results obtained by applying our quantizer in processing of neural network weights are very good matched, and, for that reason, we can expect that our proposal will find a way to practical implementation.

This brief develops a robust multiple model strategy for nonlinear system identification with system output data corrupted by outliers. The nonlinear system is described as a global model that combines multiple local nonlinear state-space models (SSMs) identified at the prechosen working points. Industrial data contaminated with outliers is a common problem in practical processes, which imposes great challenges for nonlinear processes modeling. In order to handle the outliers, the robust observation model based on Laplace distribution, instead of the conventional Gaussian distribution, is used to model the outliers corrupted output data. The approach to estimate parameters of all local models simultaneously is derived using the expectation maximization (EM) algorithm, and a particle filter (PF) is introduced to numerically calculate the cost function (Q-function) in the EM algorithm. The effectiveness of the proposed method is verified through a numerical example and the practical two-link robotic manipulator.

A Laplace ℓ1 robust student’s T-filter is presented for satellites to estimate their attitude state despite severe measurement noise and modeling error. Although the student’s T-filter (STF) has the capability of handling measurement noise, it cannot address the unknown modeling error. It is further sensitive to the degree of freedom (DOF). Hence, the measurement covariance is updated by using the maximum correntropy criterion to accommodate the covariance of unknown modeling error in robust filtering design. Moreover, the Laplace distribution is derived to reduce the influence of the DOF parameter by forming a surrogate function of an optimization problem. Then, the majorization minimization approach is formulated to solve such an optimization problem and present the proposed filtering algorithm in the STF framework. Numerical simulation of applying the proposed attitude estimation scheme is performed by comparing it with the third/fifth-order cubature Kalman filters.

We present a single-species metapopulation model structured by population size that is discrete in time. The novel formulation of our model allows for explicit incorporation of both the local, in space, dynamics and new details of the dispersal process. To study the impact of between-patch dynamics in the model, we construct various functions to describe density-dependent dispersal, recolonization, and between-patch stochasticity. Due to the complexity of the model, numerical simulations are used to obtain the distribution of the metapopulation. Moreover, we can use our model to predict the proportion of patches occupied, expected patch density, and variance in patch density. Our results provide insight into the influence that each of these processes play in the distribution of the metapopulation. In particular, our findings emphasize the benefit of explicitly modelling these processes. We consider two density-dependent dispersal strategies based upon individuals wanting to form average-sized patches and illustrate the differences in the metapopulation distributions. For recolonization of empty suitable patches, we look at two simplistic redistribution strategies modeled as either a continuous uniform or Laplace distribution. The between-patch stochasticity is modelled using redistribution kernels where we consider both thin-tailed and fat-tailed kernels. We find that the form of density-dependent dispersal has a major influence on the distribution of the metapopulation while recolonization is a key process for metapopulation persistence. In addition, fatter tails for the between-patch stochasticity can decrease the proportion of occupied patches and increase the expected patch density and variance in patch density.

This paper presents a froth image statistical modeling-based online flotation process operation-state identification method by introducing a biologically inspired Gabor wavelet transform in accordance with the physiological findings in the biological vision system. It derived the latent probabilistic density models of these biologically inspired Gabor filtering responses (GFRs) based on a versatile intermediate probability modeling frame, Gaussian scale mixture model. It has demonstrated that both the real and the imaginary representation of GFR obey a Laplace distribution. Accordingly, the amplitude representation of GFR obeys a Gamma distribution. Whereas the phase representation of GFR is an important yet frequently ignored aspect in Gabor-based signal analysis; it is demonstrated to be a periodic distribution and can be expressed by a von Mises-like distribution model. Successively, a local spline regression (LSR)-based classifier that the maps scattered statistical feature points of froth images directly to the operation-state labels smoothly is introduced for the operation-state recognition. Extensive confirmatory and comparative experiments on an industrial-scale bauxite flotation process demonstrate the effectiveness and superiority of the proposed method. Performance effects on different parameter settings, e.g., parameters of Gabor kernel and dimensionalities of multivariate statistical models, are further discussed.

Genomic prediction (GP) has become a valuable tool for predicting the performance of selection candidates for the next breeding cycle. A vast majority of statistical linear models on which GP is based rely on the assumption of normality of the residuals and therefore on the response variable itself. In this study, we propose to use Bayesian regularized quantile regression (BRQR) in the context of GP; the model has been successfully used in other research areas. We evaluated the prediction ability of the proposed model and compared it with the Bayesian ridge regression (BRR; equivalent to genomic best linear unbiased predictor, GBLUP). In addition, BLUP can be used with pedigree information obtained from the coefficient of coancestry (ABLUP). We have found that the prediction ability of BRQR is comparable to that of BRR and, in some cases, better; it also has the potential to efficiently deal with outliers. A program written in the R statistical package is available as Supplementary material.

We analyse the time evolution of the empirical cross-sectional distribution of firms’ profit and growth rates. In particular, we analyse the conditional properties of the empirical distributions depending on the size of the firms and the business cycle phase. In order to do so, we employ the Laplace distribution as a benchmark, further considering the Subbotin and Asymmetric Exponential Power (AEP hereafter) distributions, to capture the potential asymmetry and leptokurtosis of the empirical distribution. Our results show that the profit rates of large firms are characterised by an asymmetric Laplace distribution with parameters largely independent of the business cycle phase. Small firms, instead, are characterised by the AEP distribution, which accounts for the conditional dependence of distribution on the phase of the business cycle. We observe that the largest firms are more robust to downturns compared to the small firms, given their invariant distributional characteristics during crisis periods.

Pairs trading under the copula approach is revisited in this paper. It is well known that financial returns arising from indices in markets may not follow the features of normal distribution and may exhibit asymmetry or fatter tails, in particular. Due to this, the Laplace distribution is employed in this work to fit the marginal distribution function, which will then be employed in a copula function. In fact, a multivariate copula function is constructed on two indices (based on the Laplace marginal distribution), enabling us to obtain the associated probabilities required for the process of pairs trade and creating an efficient tool for trading.

A mathematical model has been introduced for the transmission dynamics of cholera disease by GQ Sun et al. recently. In this study, we add Laplacian and Triangular random effects to this model and analyze the variation of results for both cases. The expectations and co-efficients of variation are compared for the random models and the results are used to comment on the differences and similarities between the effects of these probability distributions. The randomness of the model itself is also investigated through comparison of the random and deterministic outcomes. © 2022 Academic Center for Education, Culture and Research TMU.

In this paper, a new model-based Bayesian compressive sensing technique for non-stationary images is proposed. Our algorithm is based on the recently addressed triplet Markov fields (TMF) model. The TMF model is well appropriate for non-stationary image processing, owing to the introduction of a third random field which reflects different non-stationarity of images. Furthermore, TMF can extract the interactions among the neighboring sites of an image in a more complete way than the classic hidden Markov models do. In this paper, the inter-scale dependencies between the wavelet coefficients is exploited explicitly in the proposed TMF model, which results in the wavelet domain TMF model. Our proposed model considers the intra- and inter-scale dependencies and the non-stationarity of images simultaneously. Also, we have developed our proposed algorithm for both Gaussian and non-Gaussian measurement noises, and we have modeled the non-Gaussianity of the noise via Laplace distribution. To approximate the posterior distributions of the hidden variables, we resort to a variational Bayesian expectation–maximization algorithm. Simulation results in both the optical and synthetic aperture radar images show that this model leads to an improvement over state-of-the-art algorithms in terms of the reconstruction error and the structural similarity.

The robust multimodel solution for multiple-input single-output nonlinear time-delay systems identification with polluted outputs is derived in this article. First, all the local autoregressive exogenous models are preidentified at the working points; then, the global system model is built by interpolating the local models with a smoothing strategy. The outliers and input time-delays which often increase the nonideality of process data are both considered. To cope with the outliers, the Laplace distribution is reutilized to describe the output measurement process and the negative impact resulted from each outlier imposed on parameter estimation can be suppressed through automatically assigned small weight. The parameter estimation procedure is realized with the expectation–maximization algorithm and the joint posterior probability of all input delays is also maximized to calculate the unknown input time-delays. With the verifications on a numerical example and the continuous fermentation process, the validity of the proposed approach is proved.

Block floating point quantization (BFPQ) exploits signal statistics so that one common exponent is shared among a block of data. The output signal-to-quantization-noise ratio (SQNR) may drop due to the increase in quantization error resulted from the increment of the exponent, especially for the non-uniformly distributed input signals. The tunable BFPQ is then proposed. With the aid of the tuning parameter to enlarge the thresholds for deciding the exponent and fractional exponent, the quantization error and saturation error can be balanced and thus the output SQNR can be sustained as high as possible. Both the analytic and simulated results are provided to verify the effectiveness of the tuning parameter for Gaussian-distributed and Laplacian-distributed signals. The improvement in output SQNR compared to the conventional BFPQ is also shown. Finally, the concept is implemented to support real-time high-speed compression for high-resolution synthetic aperture radar image applications. We demonstrate that the tunable BFPQ can be accomplished with only a small overhead but brings substantial performance gain, especially for large data blocks.

In this paper, we propose an alternative version to the Laplace distribution which we named as “alternative Laplace distribution (ALD)” and discuss some of its important properties. A location-scale extension of the ALD is considered and the maximum likelihood estimation procedures for estimating its parameters is described. Further, the distribution is fitted to certain real life data sets for illustrating the utility of the model. A simulation study is carried out to examine the performance of likelihood estimators of the parameters of the distribution.

A new Topp–Leone generated family of distributions, which we call the Topp–Leone Discrete Laplace ( $$TL-DL$$ ) distribution, is proposed. It has a shape parameter $$\alpha>0$$ and a scale parameter $$0

A stochastic scheme, namely, PLM-Lap, has recently been propounded, which relies on the profile likelihood (PL) constructed with a Laplace distribution for estimating muscle activation onsets (MAOs) in surface electromyographic (sEMG) data. The MAO detection accuracy and robustness of the PLM-Lap have been empirically shown to be better than those of several state-of-the-art approaches. The algorithm designates the data point index associated with the maximum of the PL function as an onset occurrence by regarding every sEMG data point as a candidate onset and hence exhaustively evaluating the objective function. This article concerns an expedient and faster approach premised on the discrete Fibonacci search (DFS) to locate the maximum of the discrete PL function. The experimental results support that both the exhaustive and DFS procedures are equivalent in a statistical sense, whereas the latter offers impressive computational savings by a factor of approximately 90. Owing to the speed-up, the accuracy of MAO estimation may further be enhanced by modeling the sEMG data with a set of PL functions, each one built using a suitable probability distribution, and picking the estimate from the best model. Three statistical criteria, i.e., Kolmogorov-Smirnov, Lilliefors, and Anderson-Darling test, for choosing the probability distribution are recommended. A freely downloadable MATLAB package, namely PROLIFIC, meant for sEMG onset detection is available on MATLAB File Exchange from the following link: https://www.mathworks.com/matlabcentral/fileexchange/76495-prolific-profile-likelihood-based-on-fibonacci-search.

Differentially private spatial decompositions split the whole domain into sub-domains recursively to generate a hierarchical private tree and add Laplace noise to each node’s points count. However the Laplace distribution is symmetric about the origin, the mean of a large number of queries may cancel the Laplace noise and reveal privacy. Existing methods take the solution by limiting the number of queries. But in private tree the points count of intermediate node may be real since the summation of all its descendants may cancel the Laplace noise. To address these problems of differentially private spatial decompositions, we propose a more secure algorithm to make the Laplace noise not be canceled. That splits the domains depending on its real points count not noisy, and only adds indefeasible Laplace noise to leaves. That the i th randomly selected leaf of one intermediate node is added noise by $\frac {\left (\upbeta -i+1 \right )+1+\upbeta }{(\upbeta -i+1)+\upbeta }Lap(\lambda )$. We also propose the definition of Lapmin(λ) whose absolute value is not greater than Sensitivity(f). It is proved that adding Lapmin(λ) noise to query answer guarantees both differential privacy and minimal relative error comparing with unlimited Laplace noise. The experiment results show that our algorithm performs better both on synthetic and real datasets with higher security and data utility, and the noises costs is highly decreased.

This paper proposes a sub-frame layer RDO algorithm to further improve coding performance of low-delay hierarchical prediction structure in High Efficiency Video Coding. In the proposed algorithm, each frame is segmented into two sub-frames according to motion intensity, and a sub-frame layer is taken as a basic optimizing unit. An inter-frame dependency model is proposed to quantify inter-frame dependency of a frame or a sub-frame. The proposed inter-frame dependency model is composed of two parts, Laplace distribution based direct inter-frame dependency model and distortion propagation chain. The direct inter-frame dependency model is used to evaluate dependency caused by direct reference, and the distortion propagation chain shows the relationship between direct reference and indirect reference. With quantified inter-frame dependency, Lagrange optimization is then used to solve the optimal $\lambda $ -QP pair for each sub-frame layer in frame layer 1 (L1) to frame layer 4 (L4). For frame layer 0 (L0), additional L0 frames are adaptively inserted according to inter-frame dependency of the previous L0 frame, and the optimal $\lambda $ -QP pair for each sub-frame in L0 is solved using Lagrange optimization. When peak signal to noise ratio is used as quality criterion, the proposed algorithm achieves 7.0% and 7.0% bit-rate reduction with lowdelay_P_main (LDP) and lowdelay_main (LDB) configurations respectively; when structural similarity is used as quality criterion, the proposed algorithm achieves 13.3% and 13.1% bit-rate reduction with LDP and LDB configurations respectively.

The traditional estimation of Gaussian mixture model is sensitive to heavy-tailed errors; thus we propose a robust mixture regression model by assuming that the error terms follow a Laplace distribution in this article. And for the variable selection problem in our new robust mixture regression model, we introduce the adaptive sparse group Lasso penalty to achieve sparsity at both the group-level and within-group-level. As numerical experiments show, compared with other alternative methods, our method has better performances in variable selection and parameter estimation. Finally, we apply our proposed method to analyze NBA salary data during the period from 2018 to 2019.

This paper is concerned with the robust parameter estimation for linear parameter varying (LPV) finite impulse response (FIR) model. The practical process data are typically polluted by outliers and conventional parameter estimation methods may fail to derive an unbiased estimate. In order to deal with outliers, the Laplace noise model is adopted and the robust system model for the described parameter estimation problem is established. The robust parameter estimation for LPV FIR model is formulated and solved in the EM algorithm scheme and the equations to estimate all the unknown parameters are derived. The efficacy of the proposed method is verified through a numerical simulation and a chemical unit.

In this paper, we study the server-side rate adaptation problem for streaming tile-based adaptive 360-degree videos to multiple users who are competing for transmission resources at the network bottleneck. Specifically, we develop a convolutional neural network (CNN)-based viewpoint prediction model to capture the nonlinear relationship between the future and historical viewpoints. A Laplace distribution model is utilized to characterize the probability distribution of the prediction error. Given the predicted viewpoint, we then map the viewport in the spherical space into its corresponding planar projection in the 2-D plane, and further derive the visibility probability of each tile based on the planar projection and the prediction error probability. According to the visibility probability, tiles are classified as viewport, marginal and invisible tiles. The server-side tile rate allocation problem for multiple users is then formulated as a non-linear discrete optimization problem to minimize the overall received video distortion of all users and the quality difference between the viewport and marginal tiles of each user, subject to the transmission capacity constraints and users' specific viewport requirements. We develop a steepest descent algorithm to solve this non-linear discrete optimization problem, by initializing the feasible starting point in accordance with the optimal solution of its continuous relaxation. Extensive experimental results show that the proposed algorithm can achieve a near-optimal solution, and outperforms the existing rate adaptation schemes for tile-based adaptive 360-video streaming., 33 pages (single column and double space) with 15 figures, submitted to IEEE Journal of Selected Topics in Signal Processing

The probabilistic neural network (PNN) is an efficient approach that can compute nonlinear decision boundaries, widely used for classification. In this paper, the often used Gaussian distribution function is replaced by a new probability density function which provides a new variant of the PNN method. Most of the higher-dimensional data are statistically found to be not from the normal distribution, and hence, we have replaced it by the symmetric Laplace distribution. Further, the estimation of the smoothing parameter in the proposed PNN model is carried out with three different evolutionary algorithms, namely bat algorithm (BA), grey wolf optimizer (GWO), and whale optimization algorithm (WOA) with a novel fitness function. These different proposed PNN models with variable smoothing parameter estimation methods are tested on five different benchmark data sets. The performance of proposed three Laplace distribution-based variants of PNN incorporated with BA, GWO, and WOA are reported and compared with Gaussian-based variants of PNN and also other commonly used classifiers: the conventional PNN, extreme learning machine, and K-nearest neighbor in terms of measurement accuracy. The results demonstrate that the proposed approaches using evolutionary algorithms can provide as much as a ten percent increase in accuracy over the conventional PNN method.

Concrete CT test is an effective method used to analyze micro-structural damage evolution of concrete under loading condition. In the CT images of different stress states in the same section, gray value changes in the original number matrix of CT image are the key to investigate microscopic damage evolution of concrete. However, the slight changes in the gray value of CT images before peak stress cannot be intuitively observed with the naked eye. This study mainly aims to develop a coupled method based on statistical method and X-ray CT to extract indicators of such subtle changes. Different cross-sectional CT images of concrete at different stress stages were obtained by uniaxial static compression CT test. The theory of the grey level co-occurrence matrices (GLCM) was then adopted to analyze micro-damage evolution and crack properties. That is, the GLCM of the CT images were calculated, and four statistical features including contrast, energy, correlation, and homogeneity were extracted, which can be extended into quantitative analysis of micro-damage hidden in the CT images of concrete. Results exhibited that the damage growth area, concentrating between the 45th and 225th concrete cross-section, could be predicted by the distribution of four statistical features (i.e., contrast, energy, correlation and homogeneity) at the fourth scan, and it is consistent with the crack location in the fifth scan. The contrast, energy and homogeneity follow the Gaussian distribution under five scan stages, and the correlation follows the Laplace distribution. In addition, the changes of bandwidth in color heat map illustrating the GLCM before and after specimen failure show that the bandwidth is positively correlated with micro-structural damage of concrete specimen.

This paper puts forward a robust identification solution for nonlinear time-delay state-space model (NDSSM) with contaminated measurements. To enhance the robustness of the developed method for outliers, the heavy-tailed Laplace distribution is employed to describe and protect the output measurement process. The undetermined time-delay is considered to be uniformly distributed and the boundary of it is known as a priori. In the developed solution, the uncertain time-delay is treated as a latent process variable and it is iteratively calculated with the expectation–maximization (EM) algorithm. The EM algorithm is actually an iterative optimization algorithm and it is effective for the hidden variable problems. The particle filter is introduced to numerically approximate the cost function (Q-function) in the EM algorithm since it is difficult to calculate directly. The efficacy of the developed solution is evaluated via a numerical test and a two-link robotic manipulator.