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The discrete Weibull model can be adapted to capture different levels of dispersion in the count data. This paper takes into account the direct relationship between explanatory variables and the median of discrete Weibull response variable. Additionally, it provides the Bayesian estimate of the discrete Weibull regression model using the random walk Metropolis algorithm. The prior distributions of the coeficient predictors were carried out based on the uniform non-informative, normal and Laplace distributions. The performance of the Bayes estimators was also compared with the maximum likelihood estimator in terms of the mean square error and the coverage probability through the Monte Carlo simulation study. Meanwhile, a real data set was analyzed to show how the proposed model and the methods work in practice. [ABSTRACT FROM AUTHOR]

Snapping Shrimps (SSs) live in a warm ocean except the North and South Poles, and they are characterized by generating strong shock waves underwater using large claws. Shock waves generated by these SSs are used for marine noise research as a signal and as a noise source, because they cause a decrease in the Signal-to-Noise Ratio (SNR), acting as one of the disruptors in fields such as sonar for target detection and underwater communication. A state-of-the-art technique to detect Snapping Shrimp Noise (SSN) is Linear Prediction (LP) analysis. Using the feature where SSN occurs for a very short time, the SSN interval was detected based on the phenomenon where the residuals appear large in the SSN interval when the LP analysis is used. In this paper, we propose an SSN interval detection technique using the Likelihood Ratio (LR) as a follow-up study to the LP-analysis-based method for further performance improvements. The proposed method was used to analyze the statistical distribution characteristics of the LP residual of SSNs compared to Gaussian, Laplace, and Gamma distributions through the Goodness-Of-Fit test. Based on this, the statistical-model-based LRs of the three distributions were computed to detect the SSN interval. Comparing the proposed method with the state-of-the-art method, the proposed method achieved 0.0620, 0.0675, and 0.0662 improvements in Gaussian, Laplace, and Gamma distributions in the Receiver Operating Characteristic curve and Area Under Curve, respectively. The study results confirmed that the proposed method can operate effectively in the marine acoustic environment. This can help find accurate intervals for the automatic labeling of or reduction in SSN. [ABSTRACT FROM AUTHOR]

Nowadays, ensuring the quality of network services has become increasingly vital. Experts are turning to knowledge graph technology, with a significant emphasis on entity extraction in the identification of device configurations. This research paper presents a novel entity extraction method that leverages a combination of active learning and attention mechanisms. Initially, an improved active learning approach is employed to select the most valuable unlabeled samples, which are subsequently submitted for expert labeling. This approach successfully addresses the problems of isolated points and sample redundancy within the network configuration sample set. Then the labeled samples are utilized to train the model for network configuration entity extraction. Furthermore, the multi-head self-attention of the transformer model is enhanced by introducing the Adaptive Weighting method based on the Laplace mixture distribution. This enhancement enables the transformer model to dynamically adapt its focus to words in various positions, displaying exceptional adaptability to abnormal data and further elevating the accuracy of the proposed model. Through comparisons with Random Sampling (RANDOM), Maximum Normalized Log- Probability (MNLP), Least Confidence (LC), Token Entrop (TE), and Entropy Query by Bagging (EQB), the proposed method, Entropy Query by Bagging and Maximum Influence Active Learning (EQBMIAL), achieves comparable performance with only 40% of the samples on both datasets, while other algorithms require 50% of the samples. Furthermore, the entity extraction algorithm with the Adaptive Weighted Multi-head Attention mechanism (AW-MHA) is compared with BILSTM-CRF,Mutil_Attention-Bilstm-Crf, Deep_Neural_Model_NER and BERT_Transformer, achieving precision rates of 75.98% and 98.32% on the two datasets, respectively. Statistical tests demonstrate the statistical significance and effectiveness of the proposed algorithms in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we study a Cauchy problem for a space-time fractional diffusion equation with exponential nonlinearity. Based on the standard Lp-Lq estimates of strongly continuous semigroup generated by fractional Laplace operator, we investigate the existence of global solutions for initial data with small norm in Orlicz space exp Lp(Rd) and a time weighted Lr(Rd) space. In the framework of the Hölder interpolation inequality, we also discuss the existence of local solutions without the Orlicz space. [ABSTRACT FROM AUTHOR]

Let s ∈ be an open bounded set. In this work we study the existence of solutions to problems (E±) Lu ± g(u) = μ and u = 0 a.e. in ℝN \ Ω, where g ∈ C(ℝ) is a nondecreasing function, μ is a bounded Radon measure on and Ω is an integro-differential operator with order of differentiability s ∈ (0, 1) and summability ... More precisely, L is a fractional p-Laplace type operator. We establish sufficient conditions for the solvability of problems (E±). In the particular case ..., these conditions are expressed in terms of Bessel capacities. [ABSTRACT FROM AUTHOR]

This manuscript presents a new two-parameter unit stochastic distribution, obtained by transforming the Laplace distribution, using a generalized logistic map, into a unit interval. The distribution thus obtained is named the Laplace-logistic unit (abbreviated LLU) distribution, and its basic stochastic properties are examined in detail. Also, the procedure for estimating parameters based on quantiles is provided, along with the asymptotic properties of the obtained estimates and the appropriate numerical simulation study. Finally, the application of the LLU distribution in dynamic and regression analysis of real-world data with accentuated “peaks” and “fat” tails is also discussed.

We study a repairable production-inventory system with a constant demand rate subject to random disruptions, which supplies an assembly line according to a just-in-time configuration. Preventive maintenance (PM) actions are regularly performed on the production unit at fixed time instants. We assume that the time between breakdowns is constant and the PM and corrective actions have random durations that follow a general probability distribution. We propose the following policy to cope with production interruptions: A buffer stock is built up at the maximum production rate at the beginning of each PM cycle. At the same time, a reserve stock is maintained to hedge against random disruptions and shortages during planned maintenance. The joint convexity of the cost function is established and optimality conditions for the optimal policy parameters are derived. We perform numerical and sensitivity analyses under the exponential and Asymmetric Laplace distributions. The results suggest that: (i) The proposed policy performs better than traditional models that consider these two strategies separately; (ii) As the shortage cost increases, it is optimal to increase the reserve level; (iii) Higher reserve stock levels allow to hedge against the increased duration and rate of preventive maintenance and random disruptions. [ABSTRACT FROM AUTHOR]

In this paper, a one-dimensional elastic–electronic deformation problem under the influence of the magnetic field will be inspected. Furthermore, the non-homogeneous (functionally graded) properties of semiconductor materials in the context of the photo-thermoelasticity theory will be studied. The hyperbolic two-temperature theory is taken into consideration during the photo-excited transport process. The interactions among the thermal, plasma, and elastic waves are analytically obtained when the optical and elastic parameters of the semiconductor medium are utilized as a function in the distance. The governing equations are formed using the Laplace transform technique to identify the analytical solutions of the key physical field distributions in the Laplace domain. Some thermal load, mechanical force, and plasma recombination conditions can be implemented at the free surface of the semiconductor medium. To illustrate the importance and effectiveness of the obtained results, the complete solutions of the main physical quantities in the space–time domain are identified using a numerical technique based on the inverse of the Laplace transform. Moreover, this work demonstrates the main physical field quantities that will be graphically represented and theoretically discussed. Many comparisons are made according to the influence of some parameters when thermal memories are taken into consideration. [ABSTRACT FROM AUTHOR]

Applications of circular regression models are ubiquitous in many disciplines, particularly in meteorology, biology and geology. In circular regression models, variable selection problem continues to be a remarkable open question. In this paper, we address variable selection in linear-circular regression models where uni-variate linear dependent and a mixed set of circular and linear independent variables constitute the data set. We consider Bayesian lasso which is a popular choice for variable selection in classical linear regression models. We show that Bayesian lasso in linear-circular regression models is not able to produce robust inference as the coefficient estimates are sensitive to the choice of hyper-prior setting for the tuning parameter. To eradicate the problem, we propose a robustified Bayesian lasso that is based on an empirical Bayes (EB) type methodology to construct a hyper-prior for the tuning parameter while using Gibbs Sampling. This hyper-prior construction is computationally more feasible than the hyper-priors that are based on correlation measures. We show in a comprehensive simulation study that Bayesian lasso with EB-GS hyper-prior leads to a more robust inference. Overall, the method offers an efficient Bayesian lasso for variable selection in linear-circular regression while reducing model complexity. [ABSTRACT FROM AUTHOR]

In recent years, deep learning has been widely employed in the field of image compression, the most significant of which is the lossy image compression method on the basis of convolutional neural networks. And we study the application of convolutional neural networks to remote sensing image compression. Consequently, we implement an enhanced residual attention module (ERAM) on the primary and hyper coders. ERAM can apply a spatial attention mechanism to generate importance masks for potential features of the original image. And the importance mask can adaptively adjust the bit distribution and allocate more bits to substantial target regions and fewer bits to unimportant background regions. Additionally, ERAM has the capacity to lessen the channel redundancy of potential features. Furthermore, an accurate probability estimate of a potential feature can affect to a great degree the effectiveness of entropy coding and hence image compression. We propose to utilise the discrete mixed Laplace entropy model to parameterize the probability distribution of latent features, which can improve the compression efficiency of latent features in the entropy encoding process. In the field of remote sensing image compression, the experiments demonstrate that the algorithm described in this paper has good subjective effects as well as good objective effects. [ABSTRACT FROM AUTHOR]

In view of the unstable electromagnetic performance of the air gap magnetic field caused by the torque ripple and harmonic interference of a multi-slot and multi-pole low-speed, high-torque permanent magnet synchronous motor, we propose a simplified model of double-layer permanent magnets. The model is divided into an upper and a lower subdomain, with the upper subdomain being an ideal circular ring and the lower subdomain being a segmented sector ring. Moreover, we develop an exact analytical model of the motor that predicts the magnetic field distribution based on Laplace's and Poisson's equations, which is solved using the method of separating variables. Taking a 40p168s low-speed, high-torque permanent magnet synchronous motor as an example, the accuracy of the model is verified by comparison with an ideal circular ring model, a segmented sector ring model, and the finite element method. Based on the proposed simplified model, three combined permanent magnets considering both edge-cutting and polar arc cutting structures are proposed, which are chamfered, rounded, and rectangular combinations. Under the premise of a consistent edge-cutting amount, the electromagnetic characteristics of the three combination types of permanent magnets are compared using the finite element method. The results show that the electromagnetic characteristics of the chamfered combination PM are superior to those of the other two combinations. Finally, a prototype is manufactured and tested to validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

Modelling skewness and heavy-tailedness in heterogeneous data sets is a compelling problem, particularly in regression analysis. The main goal of this study is to propose a mixture regression model based on the shape mixtures of skew Laplace normal (SMSLN) distribution for modelling skewness and heavy-tailedness simultaneously. The SMSLN distribution has been introduced by Doğru and Arslan [Finite mixtures of skew Laplace normal distributions with random skewness. 11th International Statistics Congress (ISC2019); Bodrum/Turkey; Finite mixtures of skew Laplace normal distributions with random skewness. Comput Stat. 2021;36(1):423–447] as a flexible extension of the skew Laplace normal (SLN) distribution and includes an extra shape parameter that controls skewness and kurtosis. The maximum likelihood estimators for the parameters of interest with the help of the expectation-maximization (EM) algorithm are obtained. The performance of the proposed mixture model is demonstrated via a simulation study and a real data example. [ABSTRACT FROM AUTHOR]

Sponsors often rely on multi‐regional clinical trials (MRCTs) to introduce new treatments more rapidly into the global market. Many commonly used statistical methods do not account for regional differences, and small regional sample sizes frequently result in lower estimation quality of region‐specific treatment effects. The International Council for Harmonization E17 guidelines suggest consideration of methods that allow for information borrowing across regions to improve estimation. In response to these guidelines, we develop a novel methodology to estimate global and region‐specific treatment effects from MRCTs with time‐to‐event endpoints using Bayesian model averaging (BMA). This approach accounts for the possibility of heterogeneous treatment effects between regions, and we discuss how to assess the consistency of these effects using posterior model probabilities. We obtain posterior samples of the treatment effects using a Laplace approximation, and we show through simulation studies that the proposed modeling approach estimates region‐specific treatment effects with lower mean squared error than a Cox proportional hazards model while resulting in a similar rejection rate of the global treatment effect. We then apply the BMA approach to data from the LEADER trial, an MRCT designed to evaluate the cardiovascular safety of an anti‐diabetic treatment. [ABSTRACT FROM AUTHOR]

We propose novel goodness-of-fit tests for the Weibull distribution with unknown parameters. These tests are based on an alternative characterizing representation of the Laplace transform related to the density approach in the context of Stein's method. Asymptotic theory of the tests is derived, including the limit null distribution, the behaviour under contiguous alternatives, the validity of the parametric bootstrap procedure, and consistency of the tests against a large class of alternatives. A Monte Carlo simulation study shows the competitiveness of the new procedure. Finally, the procedure is applied to real data examples taken from the materials science. [ABSTRACT FROM AUTHOR]

This paper is devoted to a new two‐parameter distribution on ℤ having an original additive stochastic structure. It is defined by the sum of two independent discrete random variables, where one is defined based on the Laplace distribution and the other on a transformed version of a distribution that can be viewed as a relative binomial distribution. It can thus also be viewed as a perturbed version of the Laplace distribution. We present some interesting properties of the proposed distribution, such as its moments (ordinary, non‐central, incomplete moments, etc.), characteristic function, skewness, and kurtosis, among others. The distribution is also applied to practical datasets from finance and health studies, where it is seen to perform better than some of the existing models defined on ℤ. [ABSTRACT FROM AUTHOR]

Various load balancing policies are known to achieve vanishing waiting times in the large-scale limit, that is, when the number of servers tends to infinity. These policies either require a communication overhead of one message per job or require job size information. Load balancing policies with an overhead below one message per job are called hyperscalable policies. While these policies often have bounded queue length in the large-scale limit and work well when the overhead is somewhat below one, they show poor performance when the communication overhead becomes small, that is, the mean response time tends to infinity when the overhead tends to zero even at low loads. In this paper, we introduce a hyperscalable load balancing policy, called Join-Up-To(m), that remains effective even when the communication overhead tends to zero. To study its performance under general job size distributions, we make use of the "queue at the cavity" approach. We provide explicit results for the first two moments of the response time, the generating function of the queue length distribution and the Laplace transform of the response time. These results show that the mean response time only depends on the first two moments of the job size distribution. [ABSTRACT FROM AUTHOR]

In a one-way design with unknown and unequal error variances, we are interested in testing the null hypothesis H 0 : μ 1 = μ 2 = ⋯ = μ k against the ordered alternative H 1 : μ 1 ≤ μ 2 ≤ ⋯ ≤ μ k (with at least one strict inequality). We propose the likelihood ratio test (LRT) as well as two Min-T tests (Min-T and AMin-T) and study their asymptotic behaviour. For better finite sample properties, a parametric bootstrap procedure is used. Asymptotic accuracy of the parametric bootstrap is established. Simulation results show that all the tests control the nominal level in case of small, moderate, and highly unbalanced sample sizes. This even holds for combinations with large variances. However, the asymptotic likelihood ratio test (ALRT) achieves the nominal size only for large samples and k = 3 . Power comparisons between LRT and Min-T test show that the LRT has more power than Min-T. However, the Min-T test is easier to use as it does not require evaluation of MLEs. Similar observations are made while comparing ALRT and AMin-T test. The robustness of these tests under departure from normality is also investigated by considering five non-normal distributions (t-distribution, Laplace, exponential, Weibull, and lognormal). When high variances are combined with small or highly unbalanced sample sizes, the tests are observed to be robust only for symmetric distributions. If variances of groups are equal and sample sizes of each group are at least 10, the proposed tests perform satisfactorily for symmetric and skewed distributions. R packages are developed for all tests and a practical example is provided to illustrate their application. [ABSTRACT FROM AUTHOR]

The normal inverse Gaussian (NIG) and generalized asymmetric Laplace (GAL) distributions can be seen as skewed and semi-heavy-tailed extensions of the Gaussian distribution. Models driven by these more flexible noise distributions are then regarded as flexible extensions of simpler Gaussian models. Inferential procedures tend to overestimate the degree of non-Gaussianity in the data and therefore we propose controlling the flexibility of these non-Gaussian models by adding sensible priors in the inferential framework that contract the model towards Gaussianity. In our venture to derive sensible priors, we also propose a new intuitive parameterization of the non-Gaussian models and discuss how to implement them efficiently in Stan. The methods are derived for a generic class of non-Gaussian models that include spatial Mat´ern fields, autoregressive models for time series, and simultaneous autoregressive models for aerial data. The results are illustrated with a simulation study and geostatistics application, where priors that penalize model complexity were shown to lead to more robust estimation and give preference to the Gaussian model, while at the same time allowing for non-Gaussianity if there is sufficient evidence in the data. [ABSTRACT FROM AUTHOR]

In this study, Laplace transformation, which is very important for solutions to initial value problems, is examined. To solve the initial value problem of a discrete‐time equation, Laplace implements the conversion method. Here, Laplace transformation is used to obtain an approach to the solutions of random difference equations formed by randomizing components of deterministic difference equations. For random behavior of linear difference equations under random effects, uniform, geometric, binomial, Poisson, and Bernouilli distributions are used, and approximate expected value, variance, standard deviation, and confidence interval of equations obtained by Laplace transformation are calculated. The results were obtained through the Maple package program. [ABSTRACT FROM AUTHOR]

Abstract Here we consider two-parameter and three-parameter versions of the two-tailed quasi-Lindley distribution and investigate their important properties. An attempt has been made to estimate its parameters by the method of maximum likelihood, along with a brief discussion on the existence of the estimators. Further, the distribution is fitted to certain real-life data sets to illustrate the utility of the proposed models. A simulation study is carried out to assess the performance of likelihood estimators of the parameters of the distribution. [ABSTRACT FROM AUTHOR]

By establishing a connection between a quantile regression and an asymmetric Laplace distribution (ALD), this paper considers the maximum likelihood estimation of parameters of a quantile autoregression model with Markovian switching (MSQAR), where the error terms obey ALD whose scale parameter depends on regime shifts. By utilizing the mixture representation of ALD, we develop an effective ML approach for estimating parameters of MSQAR models, and obtain closed-form estimators of unknown parameters via the EM algorithm. Consistency and asymptotic normality of estimators are shown by extending some techniques adopted in Douc, Moulines, and Rydén (2004). Also, we extend some asymptotic results of estimators to the case where the conditional quantile regression model is misspecified. Furthermore, the proposed approach is illustrated by simulations and empirical data. Simulation results show that the procedure performs well in finite samples, and the empirical analysis not only supports the existence of regime-switching in the quantile autoregression model, but also has a good performance on data fitting. [ABSTRACT FROM AUTHOR]

In this article, we define a convoluted fractional Poisson process of order k (CFPPoK), which is governed by the discrete convolution operator in the system of fractional differential equations. Next, we obtain its one-dimensional distribution by using the Laplace transform of its state probabilities. Various distributional properties, such as probability generating function, moment generating function and moments, are derived. A special case of CFPPoK, (say) convoluted Poisson process of order k (CPPoK) is studied and also established Martingale characterization for CPPoK. We further derive the covariance structure of CFPPoK and investigate the long-range dependence property. [ABSTRACT FROM AUTHOR]

We consider the process capability index (PCI), a widely used quality‐related statistic used to assess the quality of products and performance of monitored processes in various industries. It is widely known that the conventional PCIs perform well when the quality process being monitored has a normal distribution. Unfortunately, using the indices to evaluate a non‐normally distributed process often leads to inaccurate results. In this article, we consider a new PCI, Cpc$C_{pc}$, that can be used in both normal and non‐normal scenarios. The objective of this article is threefold: (i) We provide a corrected form of the confidence interval for Cpc$C_{pc}$. (ii) We compare the performance of three nonparametric bootstrap confidence intervals (BCIs) for Cpc$C_{pc}$. Specifically, the standard bootstrap, percentile bootstrap, and bias‐corrected percentile bootstrap. Under various distributional assumptions such as the normal, chi‐square, Student t, Laplace, and two‐parameter exponential distributions, the estimated coverage probabilities and average width of the confidence intervals and BCIs for Cpc$C_{pc}$ are compared. (iii) The power of the respective bootstrap approaches is evaluated by using the equivalence relation between confidence interval construction and two‐sided hypothesis testing. We also provide the receiver operating characteristic curves to evaluate their performance. Finally, as an illustrative example, an actual data set related to groove dimensions (in inches) measured from a manufacturing process of ignition keys is re‐analyzed to illustrate the utility of the proposed methods. [ABSTRACT FROM AUTHOR]

We propose flexible Bayesian quantile regression for a class of parametric nonlinear mixed effects models for longitudinal data based on the generalized asymmetric Laplace distribution, which exhibits more flexibility in skewness, mode and tail behaviour than the frequently used asymmetric Laplace distribution in quantile regression. An efficient Markov chain Monte Carlo procedure based on the adaptive random walk Metropolis-within-Gibbs sampling algorithm is derived for posterior inference. We demonstrate through simulation studies and empirical analysis that the proposed method could provide more accurate parameter estimation and better model fit than the existing methods. [ABSTRACT FROM AUTHOR]

Resetting a stochastic process is an important problem describing the evolution of physical, biological and other systems which are continually returned to their certain fixed point. We consider the motion of a subdiffusive particle with a constant drift under Poissonian resetting. In this model the stochastic process is Brownian motion subordinated by an inverse infinitely divisible process (subordinator). Although this approach includes a wide class of subdiffusive system with Poissonian resetting by using different subordinators, each of such systems has a stationary state with the asymmetric Laplace distribution in which the scale and asymmetric parameters depend on the Laplace exponent of the subordinators used. Moreover, the mean time for the particle to reach a target is finite and has a minimum, optimal with respect to the resetting rate. Features of Lévy motion under this resetting and the effect of a linear potential are discussed. [ABSTRACT FROM AUTHOR]

Laplace P-splines (LPS) combine the P-splines smoother and the Laplace approximation in a unifying framework for fast and flexible inference under the Bayesian paradigm. The Gaussian Markov random field prior assumed for penalized parameters and the Bernstein-von Mises theorem typically ensure a razor-sharp accuracy of the Laplace approximation to the posterior distribution of these quantities. This accuracy can be seriously compromised for some unpenalized parameters, especially when the information synthesized by the prior and the likelihood is sparse. Therefore, we propose a refined version of the LPS methodology by splitting the parameter space in two subsets. The first set involves parameters for which the joint posterior distribution is approached from a non-Gaussian perspective with an approximation scheme tailored to capture asymmetric patterns, while the posterior distribution for the penalized parameters in the complementary set undergoes the LPS treatment with Laplace approximations. As such, the dichotomization of the parameter space provides the necessary structure for a separate treatment of model parameters, yielding improved estimation accuracy as compared to a setting where posterior quantities are uniformly handled with Laplace. In addition, the proposed enriched version of LPS remains entirely sampling-free, so that it operates at a computing speed that is far from reach to any existing Markov chain Monte Carlo approach. The methodology is illustrated on the additive proportional odds model with an application on ordinal survey data. [ABSTRACT FROM AUTHOR]

Radiofrequency (RF) ablation represents an efficient strategy to reduce the volume of thyroid nodules. In this study, a finite element model was developed with the aim of optimizing RF parameters, e.g., input power and treatment duration, in order to achieve the target volume reduction rate (VRR) for a thyroid nodule. RF ablation is modelled as a coupled electro-thermal problem wherein the electric field is applied to induce tissue heating. The electric problem is solved with the Laplace equation, the temperature distribution is estimated with the Pennes bioheat equation, and the thermal damage is evaluated using the Arrhenius equation. The optimization model is applied to RF electrode with different active tip lengths in the interval from 5 mm to 40 mm at the 5 mm step. For each case, we also explored the influence of tumour blood perfusion rate on RF ablation outcomes. The model highlights that longer active tips are more efficient as they require lesser power and shorter treatment time to reach the target VRR. Moreover, this condition is characterized by a reduced transversal ablation zone. In addition, a higher blood perfusion increases the heat dispersion, requiring a different combination of RF power and time treatment to achieve the target VRR. The model may contribute to an improvement in patient-specific RF ablation treatment. [ABSTRACT FROM AUTHOR]

The confounding between fixed effects and (spatial) random effects in a regression setup is termed spatial confounding. This topic continues to gain attention and has been studied extensively in recent years, given that failure to account for this may lead to a suboptimal inference. To mitigate this, a variety of projection-based approaches under the class of restricted spatial models are available in the context of generalized linear mixed models. However, these projection approaches cannot be directly extended to the spatial survival context via frailty models due to dimension incompatibility between the fixed and spatial random effects. In this work, we introduce a two-step approach to handle this, which involves (i) projecting the design matrix to the dimension of the spatial effect (via dimension reduction) and (ii) assuring that the random effect is orthogonal to this new design matrix (confounding alleviation). Under a fully Bayesian paradigm, we conduct fast estimation and inference using integrated nested Laplace approximation. Both simulation studies and application to a motivating data evaluating respiratory cancer survival in the US state of California reveal the advantages of our proposal in terms of model performance and confounding alleviation, compared to alternatives. [ABSTRACT FROM AUTHOR]

In this work, a procedure to obtain two-port admittance models of buried cables illuminated by incident electromagnetic fields for the analysis of transients in the frequency domain is presented. The procedure is based on cascading two-port admittance models of various cable segments, avoiding the numerical problems that chain matrix representations may have. To obtain results in the time domain, the Numerical Laplace Transform method is used. [ABSTRACT FROM AUTHOR]

Despite the urgent need for an effective prediction model tailored to individual interests, existing models have mainly been developed for the mean outcome, targeting average people. Additionally, the direction and magnitude of covariates' effects on the mean outcome may not hold across different quantiles of the outcome distribution. To accommodate the heterogeneous characteristics of covariates and provide a flexible risk model, we propose a quantile forward regression model for high-dimensional survival data. Our method selects variables by maximizing the likelihood of the asymmetric Laplace distribution (ALD) and derives the final model based on the extended Bayesian Information Criterion (EBIC). We demonstrate that the proposed method enjoys a sure screening property and selection consistency. We apply it to the national health survey dataset to show the advantages of a quantile-specific prediction model. Finally, we discuss potential extensions of our approach, including the nonlinear model and the globally concerned quantile regression coefficients model. [ABSTRACT FROM AUTHOR]

Purpose: For quantitative susceptibility mapping (QSM), the lack of ground‐truth in clinical settings makes it challenging to determine suitable parameters for the dipole inversion. We propose a probabilistic Bayesian approach for QSM with built‐in parameter estimation, and incorporate the nonlinear formulation of the dipole inversion to achieve a robust recovery of the susceptibility maps. Theory: From a Bayesian perspective, the image wavelet coefficients are approximately sparse and modeled by the Laplace distribution. The measurement noise is modeled by a Gaussian‐mixture distribution with two components, where the second component is used to model the noise outliers. Through probabilistic inference, the susceptibility map and distribution parameters can be jointly recovered using approximate message passing (AMP). Methods: We compare our proposed AMP with built‐in parameter estimation (AMP‐PE) to the state‐of‐the‐art L1‐QSM, FANSI, and MEDI approaches on the simulated and in vivo datasets, and perform experiments to explore the optimal settings of AMP‐PE. Reproducible code is available at: https://github.com/EmoryCN2L/QSM%5fAMP%5fPE. Results: On the simulated Sim2Snr1 dataset, AMP‐PE achieved the lowest NRMSE, deviation from calcification moment and the highest SSIM, while MEDI achieved the lowest high‐frequency error norm. On the in vivo datasets, AMP‐PE is robust and successfully recovers the susceptibility maps using the estimated parameters, whereas L1‐QSM, FANSI and MEDI typically require additional visual fine‐tuning to select or double‐check working parameters. Conclusion: AMP‐PE provides automatic and adaptive parameter estimation for QSM and avoids the subjectivity from the visual fine‐tuning step, making it an excellent choice for the clinical setting. [ABSTRACT FROM AUTHOR]

Laplace probability density function with additional shape parameter that regulates the degree of skewness is a skew Laplace distribution. The various forms of skew Laplace distribution are found in the literature, the distributions defined by Mc Gill (1962), Holla and Bhattacharya (1968), Lingappaiah (1988), Fernandez and Steel (1998). The skew log Laplace distribution is the probability distribution of a random variable whose logarithm follows a skew Laplace distribution. In this paper, the classical optimum tests for skewness parameter of skew log Laplace distribution (SLLD) derived from Lingappaiah (1988) distribution are discussed. Uniformly most powerful test, uniformly most powerful unbiased test and Wald's sequential probability ratio test for skewness parameter are compared. The exact likelihood ratio test and Neyman structure test for testing skewness parameter when scale parameter is known are derived. Finally, the underreported income of Road Transport Company is analysed on the basis of the tests derived in this paper. [ABSTRACT FROM AUTHOR]

An internal heat source is assumed to act on a cylindrical body with radiation-like boundary conditions to explore the memory-dependent thermoelastic response of a solid object. The top and bottom surfaces of the solid cylinder are subjected to additional heating conditions. To obtain the thermal behaviour of the considered medium, the integral transform method is used, while the inversion solution of the heat transfer equation, the thermoelastic displacement and stress functions are presented in the Laplace domain due to the complexity of the calculation. To understand the numerical calculations, the material properties of aluminium metal are taken into account, and all the obtained results are presented graphically. [ABSTRACT FROM AUTHOR]

Introduction: Epidemiological modelling of infectious diseases plays an important role in driving public health policy. Commonly used models are described, including those based on exponential growth (Laplace and related distributions); susceptible-infected-removed; the Gompertz distribution; and the skew-reflected-Gompertz distribution. These are all sensitive to the timing of peak infection. The development of a novel method for forecasting the number of deaths occurring during epidemics of infectious diseases is described.Methods: The mathematical development of the authors' novel asymmetric difference model is detailed in this paper. Its predictions for mortality rates associated with the COVID-19 pandemic for 14 countries were compared with the corresponding published mortality data.Results: Forecasts by the asymmetric difference model of deaths from SARS-CoV-2 in different countries, actual recorded deaths to 30th June 2020, and corresponding errors included UK (42,700; 55,904; − 24%); Poland (1490; 1444; +3%); Denmark (580; 605; − 4%); Netherlands (6510; 6189; +5%); France (34,280; 29,836; +15%); Canada (1500; 8591; − 78%); USA (44,540; 124,734; − 64%); and Italy (22,020; 34,980; − 37%). The model output was dependent upon forecast date accuracy for the peak of the disease outbreak. For Spain, the forecast date was one day early and for 10 (71%) countries the forecast peak occurred within seven days (inclusive) of the actual date.Discussion: Mortality prediction by the asymmetric difference model is relatively accurate. Furthermore, this new model does not appear to be as unduly sensitive to the timing of peak infection as other models. Indeed, its prediction of peak infection also appears to be relatively accurate. [ABSTRACT FROM AUTHOR]

Abstract The Khmaladze Transformation provides a general method for transforming a parametric empirical process into an asymptotically distribution free process. Distribution free goodness of fit statistics can then be obtained from this transformed process, i.e., their limit distribution does not depend on the parametric family under consideration. However, this transformation involves inversion of incomplete Fisher information matrices and if degeneracy is present it seems at first that the transformation is no longer well-defined. The Laplace families of distributions (i.e., symmetric and asymmetric Laplace) are practically important families where this apparent complication arises. We demonstrate that even though this component of the transformation appears problematic, the transformation is still well-defined. We derive the explicit form of this transformation for these families and demonstrate with simulations that goodness of fit statistics obtained, exhibit desired distribution freeness. [ABSTRACT FROM AUTHOR]

The Laplace distribution, also known as the double exponential distribution, is a continuous probability distribution that is often used for modelling the data having heavy tails. In this paper, we proposed the Neutrosophic Laplace distribution which is the extension of the classical Laplace Distribution. We derived various statistical properties of the Neutrosophic Laplace Distribution such as mean, variance, skewness, rth moment, quartiles, and moment-generating function. The expressions for the estimation of the parameters are also derived using the maximum likelihood function of the distribution. A simulation study has been done to evaluate the performance of estimates. An application of the Neutrosophic Laplace Distribution is discussed to study the daily return of the NIFTY50 from Indian Stock Market. The analysis shows that the neutrosophic Laplace Model is acceptable, effective, and adequate for dealing with uncertainty in an unpredictable context. [ABSTRACT FROM AUTHOR]

False data injection attack (FDIA) is a deliberate modification of measurement data collected by the power grid using vulnerabilities in power grid state estimation, resulting in erroneous judgments made by the power grid control center. As a symmetrical defense scheme, FDIA detection usually uses machine learning methods to detect attack samples. However, existing detection models for FDIA typically require large-scale training samples, which are difficult to obtain in practical scenarios, making it difficult for detection models to achieve effective detection performance. In light of this, this paper proposes a novel FDIA sample generation method to construct large-scale attack samples by introducing a hybrid Laplacian model capable of accurately fitting the distribution of data changes. First, we analyze the large-scale power system sensing measurement data and establish the data distribution model of symmetric Laplace distribution. Furthermore, a hybrid Laplace-domain symmetric distribution model with multi-dimensional component parameters is constructed, which can induce a deliberate deviation in the state estimation from its safe value by injecting into the power system measurement. Due to the influence of the multivariate parameters of the hybrid Laplace-domain distribution model, the sample deviation generated by this model can not only obtain an efficient attack effect, but also effectively avoid the recognition of the FDIA detection model. Extensive experiments are carried out over IEEE 14-bus and IEEE 118-bus test systems. The corresponding results unequivocally demonstrate that our proposed attack method can quickly construct large-scale FDIA attack samples and exhibit significantly higher resistance to detection by state-of-the-art detection models, while also offering superior concealment capabilities compared to traditional FDIA approaches. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a generalization of the two-parameter double Lindley distribution (TPDLD) of Kumar and Jose [C. S. Kumar and R. Jose, A new generalization to Laplace distribution, J. Math. Comput. 31 2020, 8–32], namely the generalized double Lindley distribution (GDLD) along with its location-scale extension (EGDLD). Then we discuss the estimation of parameters of the EGDLD by the maximum likelihood estimation procedure. Next, we illustrate this estimation procedure with the help of certain real life data sets, and a simulation study is carried out to examine the performance of various estimators of the parameters of the distribution. [ABSTRACT FROM AUTHOR]

This article derives some large sample properties of weighted l1‐penalized corrected quantile estimators of the regression parameter vector in a high‐dimensional errors in variables (EIVs) linear regression model. In this model, the number of predictors p depends on the sample size n and tends to infinity, generally at a faster rate than n, as n tends to infinity. Moreover, the measurement errors in the covariates are assumed to have linear stationary temporal dependence and known Laplace marginal distribution while the regression errors are assumed to be independent non‐identically distributed random variables having possibly heavy tails. The article discusses some rates of consistency of these estimators, a model consistency result and an appropriate data adaptive algorithm for obtaining a suitable choice of weights. A simulation study assesses the finite sample performance of some of the proposed estimators. This article also contains analogs of Massart's inequality for independent and short memory moving average predictors, which is instrumental in establishing the said consistency rates of the above mentioned estimators in the current setup of high dimensional EIVs regression models. [ABSTRACT FROM AUTHOR]

We investigate the unbiased model for money exchanges with collective debt limit: agents give at random time a dollar to one another as long as they have at least one dollar or they can borrow a dollar from a central bank if the bank is not empty. Surprisingly, this dynamic eventually leads to an asymmetric Laplace distribution of wealth (conjectured in [N. Xi, N. Ding, and Y. Wang, Phys. A, 357 (2005), pp. 543--555] and shown formally in a recent work [N. Lanchier and S. Reed, J. Stat. Phys., 176 (2019), pp. 1115--1137]). In this manuscript, we carry out a formal mean-field limit as the number of agents goes to infinity where we uncover a two-phase ODE dynamic. Convergence towards the unique equilibrium (two-sided geometric) distribution in the large time limit is also shown and the role played by the bank and debt (in terms of Gini index or wealth inequality) will be explored numerically as well. [ABSTRACT FROM AUTHOR]

Intelligent manufacturing workshop uses automatic guided vehicles as an important logistics and transportation carrier, and most of the existing research adopts the intelligent manufacturing workshop layout and Automated Guided Vehicle (AGV) path step-by-step optimization, which leads to problems such as low AGV operation efficiency and inability to achieve the optimal layout. For this reason, a smart manufacturing assembly line layout optimization model considering AGV path planning with the objective of minimizing the amount of material flow and the shortest AGV path is designed for the machining shop of a discrete manufacturing enterprise of a smart manufacturing company. Firstly, the information of the current node, the next node and the target node is added to the heuristic information, and the dynamic adjustment factor is added to make the heuristic information guiding in the early stage and the pheromone guiding in the later stage of iteration; secondly, the Laplace distribution is introduced to regulate the volatilization of the pheromone in the pheromone updating of the ant colony algorithm, which speeds up the speed of convergence; the path obtained by the ant colony algorithm is subjected to the deletion of the bi-directional redundant nodes, which enhances the path smoothing degree; and finally, the improved ant colony algorithm is fused with the improved dynamic window algorithm, so as to enable the robots to arrive at the end point safely. Simulation shows that in the same map environment, the ant colony algorithm compared with the basic ant colony algorithm reduces the path length by 40% to 67% compared to the basic ant colony algorithm and reduces the path inflection points by 34% to 60%, which is more suitable for complex environments. It also verifies the feasibility and superiority of the conflict-free path optimization strategy in solving the production scheduling problem of the flexible machining operation shop. [ABSTRACT FROM AUTHOR]

The proposed study is focused to introduce a novel integral transform operator, called Generalized Bivariate (GB) transform. The proposed transform includes the features of the recently introduced Shehu transform, ARA transform, and Formable transform. It expands the repertoire of existing Laplace-type bivariate transforms. The primary focus of the present work is to elaborate fashionable properties and convolution theorems for the proposed transform operator. The existence, inversion, and duality of the proposed transform have been established with other existing transforms. Implementation of the proposed transform has been demonstrated by applying it to different types of differential and integral equations. It validates the potential and trustworthiness of the GB transform as a mathematical tool. Furthermore, weighted norm inequalities for integral convolutions have been constructed for the proposed transform operator. [ABSTRACT FROM AUTHOR]

This paper considers a retrial G-queue with collisions, transmission errors, and a finite number of sources, where service and repair time are both general distributions. The number of sources (terminals) is finite and a source cannot generate new requests until the channel (server) finishes its work, i.e., the rate at which new primary requests are generated varies inversely with the number of data frame (customer) in the system. A collision occurs when service requests arrive at a busy channel, and transmission errors prevent data frames from leaving the system after completing service. Two types of arrivals are considered. Negative customers will break down the system in the busy state and remove the customer under service. The application of our model is indicated, with a particular emphasis on communication networks such as the local-area networks (LAN) with CSMA/CD protocol. Recursive formulas have been derived to calculate the stationary joint distributions and the Laplace transform of reliability function by applying the discrete transformations method along with the supplementary variables technique (SVT). Furthermore, the comparative performance and reliability analysis have been conducted numerically. Numerical examples are provided to investigate the sensitivity of different parameters on performance measures and reliability indicators. [ABSTRACT FROM AUTHOR]

The total electron content (TEC) derived from the Global Navigation Satellite System (GNSS) has been widely used to study the ionosphere. The evaluation of the derivation method is usually based on the fitting residuals, which are the difference between the estimate and observation. However, there are few studies on the statistical characteristics of fitting residuals. The characteristics of fitting residuals and estimation errors are studied with international reference ionosphere (IRI-2016) and GNSS observations. First, the systematic estimation errors caused by mathematical modeling and related assumptions are discussed with IRI-2016. The errors are 1 TECU and 0.5 TECU for slant TEC (STEC) and vertical TEC (vTEC), respectively. The fitting residuals of STEC observations (Δ STEC r ) are studied by different noise models, including independent and identically distributed (IID) Gaussian noise, independent and non identical distributed (INID) Gaussian noise and INID Laplace noise. The statistical analysis shows that the distribution of Δ STEC r for the whole observations of all receivers is Gaussian when the noise is IID Gaussian, while it is Laplace for INID Gaussian or Laplace noise. The Δ STEC r reflects the statistical characteristic of noise. The estimation error of STEC (Δ STEC), which is the difference between the estimate ( STEC e ) and the model STEC (STEC) is discussed with IRI-2016. The distribution of Δ STEC is neither Gaussian nor Laplace, and STEC e is a biased estimate of STEC. The distribution of estimation error of vTEC (Δ vTEC) is neither Gaussian nor Laplace. Finally, the Δ STEC r is studied with GNSS observations. The distribution of Δ STEC r is more consistent with Laplace than Gaussian, indicating that the noise of the GNSS observations should not be modeled as IID Gaussian distribution. [ABSTRACT FROM AUTHOR]

The objective of this research is to propose a fuzzy solution for a specific type of uncertain fractional descriptor linear systems referred to as granular fractional descriptor linear systems (gr-FFDLSs). The coefficients, boundary conditions, and parameters in gr-FFDLSs are represented as fuzzy numbers. This type of system also encompasses the concept of fractional order granular Caputo (gr-Caputo) fuzzy derivative. To achieve this goal, the gr-Caputo fuzzy derivative of order n - 1 < β < n , where n is a natural number, is defined. Furthermore, the granular fuzzy Laplace transforms of the fractional order gr-Caputo fuzzy derivative and fractional order granular fuzzy integrals are introduced. Using the definition of fractional order gr-Caputo fuzzy derivative, fuzzy Drazin inverse matrix, and Laplace transformation, the solution to the state equation of granular descriptor fuzzy fractional linear systems is obtained. Two techniques, the fuzzy shuffle algorithm and the fuzzy Drazin inverse method, are presented to find the fuzzy solution of gr-FFDLSs. To demonstrate the effectiveness of these techniques, two examples are provided to show that they can produce accurate solutions for gr-FFDLSs. [ABSTRACT FROM AUTHOR]

Traditional convolutional neural networks (CNNs) lack equivariance for transformations such as rotation and scaling. Consequently, they typically exhibit weak robustness when an input image undergoes generic transformations. Moreover, the complex model structure complicates the interpretation of learned low- and mid-level features. To address these issues, we introduce a Lie group equivariant convolutional neural network predicated on the Laplace distribution. This model's Lie group characteristics blend multiple mid- and low-level features in image representation, unveiling the Lie group geometry and spatial structure of the Laplace distribution function space. It efficiently computes and resists noise while capturing pertinent information between image regions and features. Additionally, it refines and formulates an equivariant convolutional network appropriate for the Lie group feature map, maximizing the utilization of the equivariant feature at each level and boosting data efficiency. Experimental validation of our methodology using three remote sensing datasets confirms its feasibility and superiority. By ensuring a high accuracy rate, it enhances data utility and interpretability, proving to be an innovative and effective approach. [ABSTRACT FROM AUTHOR]

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 distributions called Tetration distribution and its subsequent tail has the property to belong to an extremely versatile family, from heavy-tailed to light-tailed. The present paper aims to construct a statistical distribution on the whole real line, based on the same principle. This new distribution, denoted Asymmetric Tetration distribution is obtained by combining a reflection of the Tetration distribution with skewing methods. Two inference methods are developed and compared in terms of performance of their estimators. In addition, an index of tail heaviness at − ∞ is proposed and computed for the most common distributions on the whole real line. Finally, the Asymmetric Tetration distribution is applied to data sets in the finance domain. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]