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In practical radar systems, changes in the target aspect toward the radar will result in glint noise disturbances in the measurement data. The glint noise has heavy-tailed characteristics and cannot be perfectly modeled by the Gaussian distribution widely used in conventional tracking algorithms. In this article, we investigate the challenging problem of tracking a time-varying number of maneuvering targets in the context of glint noise with unknown statistics. By assuming a set of models for the possible motion modes of each single-target hypothesis and leveraging the multivariate Laplace distribution to model measurement noise, we propose a robust interacting multi-model multi-Bernoulli mixture filter based on the variational Bayesian method. Within this filter, the unknown noise statistics are adaptively learned while filtering and the predictive likelihood is approximately calculated by means of the variational lower bound. The effectiveness and superiority of our proposed filter is verified via computer simulations. [ABSTRACT FROM AUTHOR]

According to the Ray-Knight description, the Brownian local time in some conditional probability space is a diffusion process with respect to spatial variable. This diffusion has a local time. Thus the following definition of local time of the original Brownian local time seems to be natural: such a process is called the second-order Brownian local time. The paper studies the Laplace transform of the distribution of the Brownian local time of the second order. [ABSTRACT FROM AUTHOR]

Lithium-ion batteries are currently used as a key energy source in various industrial facilities, electronics, and automotive industries. However, due to the frequent charging and discharging of batteries, overcharging and overdischarging can occur, leading to fire and safety accidents as well as additional financial damages due to equipment failure. Therefore, accurately estimating the battery state of charge (SOC) is very important. In this paper, the robustness of estimation models was analyzed in relation to data collected amidst sensor failures. This analysis was especially pertinent during the battery SOC estimation process, when voltage and current sensors were prone to failure. The impact of these sensor failures on the accuracy and reliability of the SOC estimation models was rigorously scrutinized. Normal data was trained as training data, and Gaussian distribution, Laplace and chi-square combined distribution, Add bias distribution were employed as the test data. Herein, multilayer neural network, long short-term memory, gated recurrent unit, gradient boosting machine (GBM) were used as neural networks, the failure signal processing performance of each estimation algorithm was compared and analyzed, and the failure diagnosis was performed using support vector machine and GBM. [ABSTRACT FROM AUTHOR]

Composite quantile regression methods have been shown to be effective techniques in improving the prediction accuracy. In this article, we propose a Bayesian weighted composite quantile regression estimation procedure to estimate unknown regression coefficients and autoregressive parameters in the linear regression models with autoregressive errors. A Bayesian joint hierarchical model is established using the working likelihood of the asymmetric Laplace distribution. Adaptive Lasso-penalized type priors are used on regression coefficients and autoregressive parameters of the model to conduct inference and variable selection simultaneously. A Gibbs sampling algorithm is developed to simulate the parameters from the posterior distributions. The proposed method is illustrated by some simulation studies and analyzing a real data set. Both simulation studies and real data analysis indicate that the proposed approach performs well. [ABSTRACT FROM AUTHOR]

Modeling longitudinal and survival data jointly offers many advantages such as addressing measurement error and missing data in the longitudinal processes, understanding and quantifying the association between the longitudinal markers and the survival events, and predicting the risk of events based on the longitudinal markers. A joint model involves multiple submodels (one for each longitudinal/survival outcome) usually linked together through correlated or shared random effects. Their estimation is computationally expensive (particularly due to a multidimensional integration of the likelihood over the random effects distribution) so that inference methods become rapidly intractable, and restricts applications of joint models to a small number of longitudinal markers and/or random effects. We introduce a Bayesian approximation based on the integrated nested Laplace approximation algorithm implemented in the R package R-INLA to alleviate the computational burden and allow the estimation of multivariate joint models with fewer restrictions. Our simulation studies show that R-INLA substantially reduces the computation time and the variability of the parameter estimates compared with alternative estimation strategies. We further apply the methodology to analyze five longitudinal markers (3 continuous, 1 count, 1 binary, and 16 random effects) and competing risks of death and transplantation in a clinical trial on primary biliary cholangitis. R-INLA provides a fast and reliable inference technique for applying joint models to the complex multivariate data encountered in health research. [ABSTRACT FROM AUTHOR]

A family of parsimonious contaminated shifted asymmetric Laplace mixtures is developed for unsupervised classification of asymmetric clusters in the presence of outliers and noise. A series of constraints are applied to a modified factor analyzer structure of the component scale matrices, yielding a family of twelve models. Application of the modified factor analyzer structure and these parsimonious constraints makes these models effective for the analysis of high-dimensional data by reducing the number of free parameters that need to be estimated. A variant of the expectation-maximization algorithm is developed for parameter estimation with convergence issues being discussed and addressed. Popular model selection criteria like the Bayesian information criterion and the integrated complete likelihood (ICL) are utilized, and a novel modification to the ICL is also considered. Through a series of simulation studies and real data analyses, that includes comparisons to well-established methods, we demonstrate the improvements in classification performance found using the proposed family of models. [ABSTRACT FROM AUTHOR]

This research delves into the exploration of a statistical testing approach grounded in Laplace transform techniques specifically tailored for the New Better than Used Laplace transform order (NBUL) class of life distributions. The developed test exhibits versatility, accommodating both complete and censored data, and critical values are systematically calculated for its application. Beyond the methodological presentation, our study investigates the test's statistical power and explores Pitman's asymptotic efficiency concerning various alternative distributions. Comparative analyses with other tests within the same class contribute to a comprehensive understanding of the proposed approach. To demonstrate practical applicability, we apply this novel testing technique to authentic engineering and medical datasets. The outcomes of these applications serve as illustrative examples, showcasing the effectiveness and relevance of the proposed methodology in real-world scenarios. [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]

Two new non convex penalty functions – Laplace and arctan – were recently introduced in the literature to obtain sparse models for high-dimensional statistical problems. In this article, we study the theoretical properties of Laplace and arctan penalized ordinary least squares linear regression models. We first illustrate the near-unbiasedness of the non zero regression weights obtained by the new penalty functions, in the orthonormal design case. In the general design case, we present theoretical results in two asymptotic settings: (a) the number of features, p fixed, but the sample size, n → ∞ , and (b) both n and p tend to infinity. The theoretical results shed light onto the differences between the solutions based on the new penalty functions and those based on existing convex and non convex Bridge penalty functions. Our theory also shows that both Laplace and arctan penalties satisfy the oracle property. Finally, we also present results from a brief simulations study illustrating the performance of Laplace and arctan penalties based on the gradient descent optimization algorithm. [ABSTRACT FROM AUTHOR]

We consider how a population of N haploid individuals responds to directional selection on standing variation, with no new variation from recombination or mutation. Individuals have trait values z 1 , ... , z N , which are drawn from a distribution ψ ; the fitness of individual i is proportional to e z i . For illustration, we consider the Laplace and Gaussian distributions, which are parametrised only by the variance V 0 , and show that for large N , there is a scaling limit which depends on a single parameter N V 0 . When selection is weak relative to drift (N V 0 ≪ 1), the variance decreases exponentially at rate 1 / N , and the expected ultimate gain in log fitness (scaled by V 0 ), is just N V 0 , which is the same as Robertson's (1960) prediction for a sexual population. In contrast, when selection is strong relative to drift (N V 0 ≫ 1), the ultimate gain can be found by approximating the establishment of alleles by a branching process in which each allele competes independently with the population mean and the fittest allele to establish is certain to fix. Then, if the probability of survival to time t ∼ 1 / V 0 of an allele with value z is P (z) , with mean P ¯ , the winning allele is the fittest of N P ¯ survivors drawn from a distribution ψ P / P ¯. The expected ultimate change is ∼ 2 log (1. 15 N V 0 ) for a Gaussian distribution, and ∼ − 1 2 log 0. 36 N V 0 − log − log 0. 36 N V 0 for a Laplace distribution. This approach also predicts the variability of the process, and its dynamics; we show that in the strong selection regime, the expected genetic variance decreases as ∼ t − 3 at large times. We discuss how these results may be related to selection on standing variation that is spread along a linear chromosome. [ABSTRACT FROM AUTHOR]

High‐breakdown‐point estimators of multivariate location and shape matrices, such as the MM‐estimator with smoothed hard rejection and the Rocke S‐estimator, are generally designed to have high efficiency for Gaussian data. However, many phenomena are non‐Gaussian, and these estimators can therefore have poor efficiency. This article proposes a new tunable S‐estimator, termed the Sq‐estimator, for the general class of symmetric elliptical distributions, a class containing many common families such as the multivariate Gaussian, t‐, Cauchy, Laplace, hyperbolic, and normal inverse Gaussian distributions. Across this class, the Sq‐estimator is shown to generally provide higher maximum efficiency than other leading high‐breakdown estimators while maintaining the maximum breakdown point. Furthermore, the Sq‐estimator is demonstrated to be distributionally robust, and its robustness to outliers is demonstrated to be on par with these leading estimators while also being more stable with respect to initial conditions. From a practical viewpoint, these properties make the Sq‐estimator broadly applicable for practitioners. These advantages are demonstrated with an example application—the minimum‐variance optimal allocation of financial portfolio investments. [ABSTRACT FROM AUTHOR]

Seismic b-value is one of the most important parameters for seismological research and seismic hazards assessment, while the accuracy of the b-value largely depended on the completeness of seismic catalog. This article compares eight methods for estimating the minimum magnitude of completeness (Mc). The results indicate that the modified maximum curvature method (MMAXC), exhibits greater stability and accuracy, closely approximating the standard M[sub c] obtained from the synthetic seismic catalogs. We then calculate the b-value using the instrumental seismic catalog from 2000-2023 in the eastern Tibetan Plateau. The results indicate that the five major earthquakes occur in regions with lower b-value. In addition, the temporal evolution of b-value before and after major earthquakes exhibits a common trend of decreasing before earthquakes, and increasing after earthquakes, which may reflect the stress accumulation and release during earthquakes. Combining the results of maximum shear strain rate and b-value, we identify five regions characterized by low b-value and high shear strain rate, indicating a higher potential seismic hazard in the future. [ABSTRACT FROM AUTHOR]

We investigate the stochastic unstable nonlinear Schrödinger equation through bi-random sources. Specifically, we solve this equation via Itô sense, with the parameter following Laplace and Gumbel distributions. We provide vital stochastic solutions in applied sciences. We employ He's semi-inverse technique in order to provide these solutions in a unified way. Actually, this is the first time that the same model has been taken into account in these circumstances. In order to investigate the real relevance of the stochastic unstable nonlinear Schrödinger equation, we provide the simulations for some of the collected solutions using the appropriate parameter settings provided by the MATLAB software. Finally, our renewed drive might expand to incorporate further emerging natural science models. [ABSTRACT FROM AUTHOR]

Motivated by queueing applications, we study various reflected autoregressive processes with dependencies. Among others, we study cases where the interarrival and service times are proportionally dependent on additive and/or subtracting delay, as well as cases where interarrival times depend on whether the service duration of the previous arrival exceeds or not a random threshold. Moreover, we study cases where the autoregressive parameter is constant as well as a discrete or a continuous random variable. More general dependence structures are also discussed. Our primary aim is to investigate a broad class of recursions of autoregressive type for which several independence assumptions are lifted and for which a detailed exact analysis is provided. We provide expressions for the Laplace transform of the waiting time distribution of a customer in the system in terms of an infinite sum of products of known Laplace transforms. An integer-valued reflected autoregressive process that can be used to model a novel retrial queueing system with impatient customers and a general dependence structure is also considered. For such a model, we provide expressions for the probability generating function of the stationary orbit queue length distribution in terms of an infinite sum of products of known generating functions. A first attempt towards a multidimensional setting is also considered. [ABSTRACT FROM AUTHOR]

We present a novel depth from focus technique. Following prior work, our pipeline starts with a focal stack and an estimation of the amount of defocus as given by, for instance, the ring difference filter. To improve robustness to outliers while avoiding to rely on costly nonlinear optimizations, we propose an original scheme that linearly scans the profile over a fixed size window, searching for the best peak within each window using a linearized least-squares Laplace regression. As a post-process, depth estimates with low confidence are reconstructed though an adaptive moving least squares filter. We show how to objectively evaluate the performance of our approach by generating synthetic focal stacks from which the reconstructed depth maps can be compared to ground truth. Our results show that our method achieves higher accuracy than previous nonlinear Laplace regression technique, while being orders of magnitude faster. [ABSTRACT FROM AUTHOR]

Regression model is a popular and well-acknowledged technique for finding a relationship between random phenomena. In this context, the normality assumption on the error terms is one of the challenging issues in practical studies because many phenomena in the real world are prone to skewness, peakness, and outliers. In this paper, a new generalization of nonlinear regression models is postulated by considering asymmetric Laplace distribution on the error terms to cover the drawbacks of the normal-based model in accommodating skew data with peakness and mild outliers. We present three stochastic representations of the model which enables us to develop an expectation–maximization (EM) algorithm to computationally obtain the maximum-likelihood (ML) parameter estimates. The observed information matrix is computed by adopting an information-based approach. The Bayesian analysis for the proposed model is also investigated. Finally, experiments on the simulation and real-world datasets illustrate some computational and robust aspects of the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, we first develop exact likelihood inference for Laplace distribution based on a generalized Type-I hybrid censored sample (Type-I HCS). We derive explicit expressions for the maximum likelihood estimators (MLEs) of the location and scale parameters. We then derive the joint moment generating function (MGF) of the MLEs, and use it to obtain the exact distributions and moments of the MLEs. Using an analogous approach, we extend the results to a generalized Type-II hybrid censored sample (Type-II HCS) next. Finally, we present a numerical example to illustrate all the results established here. [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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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 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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]