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Competing risks data arise when occurrence of an event hinders observation of other types of events, and they are encountered in various research areas including biomedical research. These data have been usually analyzed using the hazard-based models, not survival times themselves. In this paper, we propose a joint accelerated failure time (AFT) modeling approach to model clustered competing risks data. Times to competing events are assumed to be log-linear with normal errors and correlated through a scaled random effect that follows a zero-mean normal distribution. Inference on the model parameters is based on the h-likelihood. Performance of the proposed method is evaluated through extensive simulation studies. The simulation results show that the estimated regression parameters are robust against the violation of the assumed parametric distributions. The proposed method is illustrated with three real competing risks data sets. [ABSTRACT FROM AUTHOR]

The modality is an important topic for modelling. Using parametric models is an efficient way when real data set shows trimodality. In this paper, we propose a new class of trimodal probability distributions, that is, probability distributions that have up to three modes. Trimodality itself is achieved by applying a proper transformation to density function of certain continuous probability distributions. At first, we obtain preliminary results for an arbitrary density function $ g(x) $ g (x) and, next, we focus on the Gaussian case, studying trimodal Gaussian model more deeply. The Gaussian distribution is applied to produce the trimodal form of Gaussian known as normal distribution. The tractability of analytical expression of normal distribution and properties of the trimodal normal distribution are important reasons why we choose normal distribution. Furthermore, the existing distributions should be improved to be capable of modelling efficiently when there exists a trimodal form in a data set. After new density function is proposed, estimating its parameters is important. Since Mathematica 12.0 software has optimization tools and important modelling techniques, computational steps are performed using this software. The bootstrapped form of real data sets are applied to show the modelling ability of the proposed distribution when real data sets show trimodality. [ABSTRACT FROM AUTHOR]

Measuring economic inequality is an important topic to explore the social system. The Gini index and Pietra ratio are used by many people but are limited to reflecting the sampling distribution. In this paper, we study the interval estimates with another measure called the lower mean ratio u. By using jackknife empirical likelihood (JEL), adjusted jackknife empirical likelihood (AJEL), mean jackknife empirical likelihood (MJEL), mean adjusted jackknife empirical likelihood (MAJEL), and adjusted mean jackknife empirical likelihood methods, we propose the interval estimator for u. In the simulation study, we make a comparison of these methods in terms of coverage probability and average confidence interval length. The simulation results indicate that MAJEL performs the best among these methods for small sample sizes of the skewed distribution. For a small sample size of normal distribution, both JEL and MJEL show better performance than the other methods but MJEL is relatively time-consuming. Finally, two real data sets are analysed to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

A two-sided sequential probability ratio test (SPRT) control chart for monitoring the mean of a normal process is proposed in this paper. Its mechanism is based on the SPRT for the mean of a normal distribution that is extended for a two-sided alternative. The exact statistical performance measures of this chart are obtained using a Markov chain approach. An approach to design the chart such that it has a specified in-control performance and the optimal out-of-control performance for detecting a mean shift of a particular size is provided. The statistical performance of this chart is numerically compared with that of various competing charts in the existing literature. It is found that the proposed chart outperforms all these charts for detecting a mean shift of any size. An example to illustrate the mechanism of the chart is provided. [ABSTRACT FROM AUTHOR]

QR decomposition is widely used for solving the least squares problem. However, existing materials about it may be too abstract for non-mathematicians, especially STEM students, and/or require serious background in linear algebra. The paper describes theoretical background and examples of GNU Octave compatible MATLAB scripts that give relatively simple but complete explanations about how to use QR decomposition for the least squares problem solution. Only basic knowledge of linear algebra and calculus are required. Both Givens rotations and Householder reflections usage for the linear least squares problem were considered. It was shown that the algorithm based on Givens rotations is even easier to program than explicit formation of the normal equations with subsequent usage of Gaussian elimination. [ABSTRACT FROM AUTHOR]

The Lilliefors test of normality is a popular and easy-to-explain method for testing whether a sample comes from a normal distribution. Unfortunately, since it relies on the sample mean and sample standard deviation for estimating the parameters of the normal distribution, the Lilliefors test is quite sensitive to the presence of outliers. Contrarily to what could be expected, the substitution of the estimators of location and scale by robust alternatives still does not suffice for obtaining a robust method when either the number of outliers or the sample size is large. In this paper, we propose an actual robust alternative relying on classical and data-driven trimming techniques. The presented test depends on the choice of a subsetting technique, of which we explore three possibilities, and of one parameter, which models the robustness of the test in the presence of outliers. As expected, the choice of parameter is a delicate issue since the gain in robustness comes at the price of a reduced power against some types of alternatives. [ABSTRACT FROM AUTHOR]

This paper estimates a correlation model and joint distribution model of spectral accelerations of vertical ground motions based on the NGA-West2 ground motion database. The correlation model calculated via BC16 vertical GMPE in this study is compared with those published models via other vertical NGA-West2 GMPEs. It is verified that the calculated residuals of vertical ground motions at multiple periods follow the multivariate normal distributions via both a qualitative validation method and a set of quantitative validation methods. The correlation model and the joint distribution model of vertical spectral accelerations are the theoretical basis for research on the joint occurrence of spectral accelerations of vertical ground motions, and an example of applied research on joint occurrence of spectral accelerations of vertical ground motions is studied: the conditional mean spectrum of vertical ground motions. Finally, the effects of different vertical correlation models and ground motion prediction equations on vertical conditional spectra are investigated for wide application of the correlation model and the joint distribution model of spectral accelerations of vertical ground motions. [ABSTRACT FROM AUTHOR]

Finite mixture of linear regression (FMLR) models are an efficient tool to fit the unobserved heterogeneous relationships. The parameter estimation of FMLR models is usually based on the normality assumption, but it is very sensitive to outliers. Meanwhile, the traditional robust methods often need to assume a specific error distribution, and are not adaptive to dataset. In this paper, a robust estimation procedure for FMLR models is proposed by assuming that the error terms follow an asymmetric exponential power distribution, including normal distribution, skew-normal distribution, generalized error distribution, Laplace distribution, asymmetric Laplace distribution, and uniform distribution as special cases. The proposed method can select the suitable loss function from a broad class in a data driven fashion. Under some conditions, the asymptotic properties of proposed method are established. In addition, an efficient EM algorithm is introduced to implement the proposed methodology. The finite sample performance of the proposed approach is illustrated via some numerical simulations. Finally, we apply the proposed methodology to analyze a tone perception data. [ABSTRACT FROM AUTHOR]

This paper proposes using Gram-Charlier Type A probability distributions to measure solvency risk. The method assesses the likelihood of a bank's solvency falling below the minimum ratio set by regulators. Applied to 15 banks in Colombia, the study reveals the importance of considering the proximity of the Capital Adequacy Ratio (CAR) to the regulatory minimum and the probability distribution of solvency changes. Gram-Charlier Type A functions offer a better fit than the normal distribution. These findings hold significance for regulators and decision-makers, emphasizing the need to incorporate suitable measures for assessing solvency risk in banks. [ABSTRACT FROM AUTHOR]

Linear Mixed Effects (LME) models have been widely applied in clustered data analysis in many areas including marketing research, clinical trials, and biomedical studies. Inference can be conducted using maximum likelihood approach if assuming Normal distributions on the random effects. However, in many applications of economy, business and medicine, it is often essential to impose constraints on the regression parameters after taking their real-world interpretations into account. Therefore, in this paper we extend the classical (unconstrained) LME models to allow for sign constraints on its overall coefficients. We propose to assume a symmetric doubly truncated Normal (SDTN) distribution on the random effects instead of the unconstrained Normal distribution which is often found in classical literature. With the aforementioned change, difficulty has dramatically increased as the exact distribution of the dependent variable becomes analytically intractable. We then develop likelihood-based approaches to estimate the unknown model parameters utilizing the approximation of its exact distribution. Simulation studies have shown that the proposed constrained model not only improves real-world interpretations of results, but also achieves satisfactory performance on model fits as compared to the existing model. [ABSTRACT FROM AUTHOR]

The minimum covariance determinant (MCD) estimate is an important subsample method in robust statistics. It is commonly used to estimate parameters of multivariate normal distributions when outliers exist because of its good robustness properties. However, MCD has some disadvantages including low efficiency when there is no outliers and poor performance when there are clustered outliers. This paper first introduces an adaptive subsample method, and shows that the adaptive MCD estimator can possess both full asymptotic efficiency and maximum breakdown value. We then propose a minimum distance subsample estimate to handle the situations where there are clustered outliers. Simulation results indicate that the adaptive version of the minimum distance subsample estimate has satisfactory performance for various types of outliers. [ABSTRACT FROM AUTHOR]

This paper introduces a robust procedure for controlling the false discovery rate utilizing empirical likelihood. Traditional approaches assume a normal or parametric distribution as the null distribution. However, it may be challenging to constrain the null distribution within specific parametric models. We focus on the cases where the null distribution may not precisely follow a normal distribution. Multiple testing procedures based on exact normality can lead to misleading outcomes. To address this issue, we adopt the empirical likelihood to estimate the null distribution. Additionally, we introduce the concept of a pilot distribution to establish constraints on the null distribution, which aids in estimating the empirical null distribution. We present a fast algorithm and provide theoretical justification for its efficiency. Furthermore, simulation studies demonstrate that our method outperforms existing approaches in controlling the false discovery rate. We also include examples involving gene expression data and compare the performance of different methods. [ABSTRACT FROM AUTHOR]

Many classical methods have been proposed to compute circular-circular correlation coefficients. However, these classical methods might be very sensitive to outliers in the data set. To date, no work has suggested a robust method to estimate a circular-circular correlation coefficient. The present paper aims to propose two robust methods to compute a circular-circular correlation coefficient when the circular data has outliers. The first method is computed based on the circular median, rMed, and the second on the circular trimmed mean, rTrim. A simulation study is conducted for two circular distributions: the wrapped normal and wrapped Cauchy distributions. The simulation and practical example show that the results of rMed are close to the results of classical methods. In contrast, the rTrim gives the best results and is the least affected by outliers, even with a high percentage of outliers. [ABSTRACT FROM AUTHOR]

In recent years, more attention has been paid prominently to accelerated degradation testing (ADT) in order to characterize accurate estimation of reliability properties for systems that are designed to work properly for years or even decades. In this paper, we propose optimal experimental designs for repeated measures ADTs with competing failure modes that correspond to multiple response components. The marginal degradation paths are expressed using linear mixed effects models. The optimal design is obtained by minimizing the asymptotic variance of the estimator of some quantile of the failure time distribution at the normal use conditions. Numerical examples are introduced to ensure the robustness of the proposed optimal designs and compare their efficiency with standard experimental designs. [ABSTRACT FROM AUTHOR]

This paper estimates the joint occurrence of spectral accelerations (SA) between horizontal (HGM) and vertical ground motions (VGM) based on the NGA-West2 ground motion database, which includes the correlation model and joint distribution model. In this study, the correlation model calculated via CB14 horizontal ground motion prediction equation (GMPE) and BC16 vertical GMPE is obtained. It is verified that the joint distribution of residuals follows a multivariate normal distribution via both a set of quantitative validation methods and a qualitative validation method. Conditional mean spectra of VGMs conditioned on SAs of HGMs are studied as an application of joint occurrence of SAV–SAH. [ABSTRACT FROM AUTHOR]

Acceptance sampling is one of the most important tools in quality control, and it has been extensively used in the industry for inspecting received lots. As different situations and purposes could be encountered in real life, numerous approaches for sampling plans have been established. When the quality of the process is good and stable, Skip-lot sampling plans (SkSPs) are useful strategies of sampling and could be an advantageous examination scheme. Therefore, this paper aims to incorporate the process yield index for a first-order autoregressive process S p k ; A R (1) and the SkSP, when the quality characteristic follows a normal distribution with bilateral specification limits, to produce a variables Skip lot sampling plan of type 2 (SkSP-2) with a single sampling plan (SSP) based on S p k ; A R (1) as the reference plan. A non-linear optimization model is solved to decide the plan parameters, by fulfiling the quality and risk obligations identified by the manufacturer and buyer and minimizing the average sample number (ASN). We investigated the efficiency and performance of the suggested SkSP-2 S p k ; A R (1) -based, associated with the variables SSP in terms of average sample number curves and the operating characteristic. Furthermore, the plan parameters with particular conditions are delivered for reference as tables, and an industrial application is offered to prove the applicability of the proposed plan. [ABSTRACT FROM AUTHOR]

In recent years, the study of Receiver Operating Characteristic (ROC) curve analysis has gained significant attention as a means of accurately assessing test performance and determining optimal cutoff points. Traditionally, ROC models have been developed for bi-distributional univariate and multivariate data, such as Bi-normal, Bi-Exponential, Multivariate ROC models, and so forth. However, in current practical scenarios, the prevalence of high-dimensional matrix variate data poses a challenge for accurate test evaluation. To address this issue, this paper presents a novel ROC model that incorporates matrix variate normal distribution to effectively explain the accuracy of a test in the context of matrix data. Further, the accuracy measure, Area under the Curve (AUC) is derived, which helps in explaining the variability of the curve and provides the sensitivity at a particular value of specificity and vice versa. The proposed methodology is supported by a real data set and simulation studies. [ABSTRACT FROM AUTHOR]

In this paper, we propose Multi-View Dreaming, a novel reinforcement learning agent for integrated recognition and control from multi-view observations by extending Dreaming. Most current reinforcement learning method assumes a single-view observation space, and this imposes limitations on the observed data, such as lack of spatial information and occlusions. This makes obtaining ideal observational information from the environment difficult and is a bottleneck for real-world robotics applications. In this paper, we use contrastive learning to train a shared latent space between different viewpoints and show how the Products of Experts approach can be used to integrate and control the probability distributions of latent states for multiple viewpoints. We also propose Multi-View DreamingV2, a variant of Multi-View Dreaming that uses a categorical distribution to model the latent state instead of the Gaussian distribution. Experiments show that the proposed method outperforms simple extensions of existing methods in a realistic robot control task. [ABSTRACT FROM AUTHOR]

In this paper we describe a methodology for parameter estimation of multivariate distributions defined as normal mean-variance mixture where the mixing random variable is rapidly decreasing tempered stable distributed. We address some numerical issues resulting from the use of the characteristic function for density approximation. We focus our attention on the practical implementation of numerical methods involving the use of these multivariate distributions in the field of finance and we empirical assess the proposed algorithm through an analysis on a five-dimensional series of stock index log-returns. [ABSTRACT FROM AUTHOR]

Probabilistic principal component analysis (PPCA) is a probabilistic reformulation of principal component analysis (PCA), under the framework of a Gaussian latent variable model. To improve the robustness of PPCA, it has been proposed to change the underlying Gaussian distributions to multivariate t-distributions. Based on the representation of t-distribution as a scale mixture of Gaussian distributions, a hierarchical model is used for implementation. However, in the existing literature, the hierarchical model implemented does not yield the equivalent interpretation. In this paper, we present two sets of equivalent relationships between the high-level multivariate t-PPCA framework and the hierarchical model used for implementation. In doing so, we clarify a current misrepresentation in the literature, by specifying the correct correspondence. In addition, we discuss the performance of different multivariate t robust PPCA methods both in theory and simulation studies, and propose a new Monte Carlo expectation-maximization (MCEM) algorithm to implement one general type of such models. [ABSTRACT FROM AUTHOR]

This paper proposes a normalizing transformation of the Dempster statistic for testing the equality of two mean vectors with unequal covariance matrices in high-dimensional settings. The distribution of the Dempster statistic is known to converge to a normal distribution as dimension p goes to infinity; however, its rate of convergence is not guaranteed. Therefore, normal approximation is often too loose for medium p settings or fails to capture the tail behavior of the resulting distribution. We developed a concept of normalizing transformation of a statistic based on the rate of convergence to normality and show that the rate of convergence to normality is improved by normalizing transformation of the Dempster statistic. [ABSTRACT FROM AUTHOR]

The beta generator technique entails constructing a univariate distribution function as a composite function of two distribution functions. The success of this technique in the univariate setting has prompted research into the possibility of generalization to the bivariate case. Such a generalization, using copulas, has already been proposed in the literature. In this paper, we construct bivariate distribution functions by passing a bivariate distribution function as an argument to the univariate beta distribution function. The class of distributions obtained is identical to an existing class of distributions; however, the elementary elements of the two classes differ (i.e., some distributions are simple to construct using one of the techniques considered and difficult to construct using the other). This paper provides a rigorous derivation of the parameter space of the beta-generated distributions, as well as a result relating to the dependence structure of the marginals. Finally, a practical example is included demonstrating the use of a beta-generated distribution in the modeling of observed losses in the energy market. [ABSTRACT FROM AUTHOR]

Empirical likelihood has been widely used in survival data analysis recently. In this paper, we combine Bayesian idea with empirical likelihood and develop a Bayesian empirical likelihood method to analyze current status data based on the linear regression model. By constructing unbiased transformation of current status data, we derive an empirical log-likelihood function. The normal prior distribution and a Metro-Hastings method are presented to make Bayesian posterior inference. The theoretical properties of the estimators are proposed. Extensive simulation studies indicate that Bayesian empirical likelihood method performs much better than the empirical likelihood method in terms of coverage probability. Finally, we apply two real data to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the filtering issues are investigated for wireless networked control systems (WNCSs) with Markovian packet losses. In WNCSs, Markovian packet losses often occur in both control and feedback channels, and User Datagram Protocol (UDP) is usually used to ensure real-time control and energy saving. First, the optimal filtering algorithm for WNCSs with Markovian packet losses is obtained. However, it cannot be applied in practice as its running time increases exponentially with time. Then a computationally efficient filtering algorithm is developed by approximating the probability density function of the estimated value to a Gaussian distribution, where the approximation is obtained by minimising the Kullback-Leibler divergence (KLD). Finally, the upper and lower bounds of the performance of the KLD-based approximate filter and sufficient conditions of its stability are obtained. Numerical examples are given to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The Lévy distribution, alongside the Normal and Cauchy distributions, is one of the only three stable distributions whose density can be obtained in a closed form. However, there are only a few specific goodness-of-fit tests for the Lévy distribution. In this paper, two novel classes of goodness-of-fit tests for the Lévy distribution are proposed. Both tests are based on V-empirical Laplace transforms. New tests are scale free under the null hypothesis, which makes them suitable for testing the composite hypothesis. The finite sample and limiting properties of test statistics are obtained. In addition, a generalization of the recent Bhati–Kattumannil goodness-of-fit test to the Lévy distribution is considered. For assessing the quality of novel and competitor tests, the local Bahadur efficiencies are computed, and a wide power study is conducted. Both criteria clearly demonstrate the quality of the new tests. The applicability of the novel tests is demonstrated with two real-data examples. [ABSTRACT FROM AUTHOR]

In this paper a new family of Harris skewed normal distributions (HSND) is proposed. The probability density function of the HSND can be both positively and negatively skewed, unimodal and multimodal and can be symmetric with heavy tails. Monte Carlo simulations are conducted to evaluate the applicability of the proposed family of distributions. The HSND family is used to fit three different real data sets. [ABSTRACT FROM AUTHOR]

In a simultaneous localization and mapping (SLAM) system, in general, distribution estimation based on a particle filter is used for localization of Unmanned Ground Vehicle (UGV) with a laser rangefinder, and point estimation based on optimization is used for Unmanned Aerial Vehicle (UAV) with a monocular camera. In order for such robots to perform cooperative localization to improve accuracy, it is necessary to convert the localization results of point estimation and distribution estimation into a format that can be introduced to each other. In this paper, we propose an integration method of estimation results for cooperative localization by UAV and UGV. The UAV point estimation result is converted to a normal distribution by giving a fixed covariance matrix in order to introduce it as the observation likelihood of the UGV. On the other hand, the particle pose with maximum weight obtained from the UGV distribution estimation result is added to the current pose constraint in UAV optimization. As a result, this allows stable localization of both by correcting with the estimation result of the other even in an environment where either one is disadvantageous for localization. [ABSTRACT FROM AUTHOR]

Multivariate regression models are helpful in many fields. However, independent variables (covariates or predictors) could be measured with error. That implies the necessity of considering a new kind of model called Multivariate Regression Models with Measurement Error (MRMMEs). This paper aims to carry out a statistical analysis of these models. We include estimation, hypothesis testing, model assessment, and influence diagnostics. Furthermore, besides considering the classical assumption of the normal distribution, we use maximum likelihood for the whole inference process. Finally, we study the developed approach's performance through simulation experiments and re-analyze the human lung function dataset presented in the literature to illustrate the methodology. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic distribution of the plug-in kernel density estimator of the Matusita's overlapping measure. By utilizing the convergence of functional of stochastic processes, we show, under certain conditions, that the asymptotic distribution of the plug-in kernel density estimator (KDE) of Matusita's overlapping measure is normal distribution. Also, a small simulation study is conducted to support the theoretical finding of this paper. Furthermore, we apply our finding to a breast cancer data. [ABSTRACT FROM AUTHOR]

The reliability analysis for the system with degradation and random shocks is an important issue in the field of reliability engineering. In this paper, we use Wiener process to fit the performance degradation process, and regard both the degradation rate and the mean of the magnitude of shock load as random variables which follow the truncated normal distribution. With the Markov Chain Monte Carlo(MCMC), we provide a new method to estimate the parameters of the reliability function of the system. At the end of the paper, we take the degradation and shock data of the MOSFET as an example to show the effectiveness of the method presented in the paper. [ABSTRACT FROM AUTHOR]

In this paper, an economic statistical design for individual samples of quality characteristics which have Exponential distributions presented with variable sampling method. To do this, first the Exponential distribution is transformed to a Normal distribution Using Nelson's approximation, then using Costa and Rahim's economic model, an economic statistical design is obtained for the transformed data. The transition probability matrix and the economic and statistical parameters are formulated. Optimal design parameters (sampling interval, warning and control limits) are determined using Artificial Bee Colony algorithm and a sensitivity study is done for various values of the model parameters. Based on the results, the mentioned method in compared with the fixed ratio sampling method is more effective when a moderate shift occurs. A simulated example is given also to illustrate the proposed design. [ABSTRACT FROM AUTHOR]

In production design processes, multiple correlated responses with different distributions are often encountered. The existing literature usually assumes that they follow normal distributions for computational convenience, and then analyzes these responses using traditional parametric methods. A few research papers assume that they follow the same type of distribution, such as the t-distribution, and then use a multivariate joint distribution to deal with the correlation. However, these methods give a poor approximation to the actual problem and may lead to the recommended settings that yield substandard products. In this article, we propose a new method for the robust parameter design that can solve the above problems. Specifically, a semiparametric model is used to estimate the margins, and then a joint distribution function is constructed using a multivariate copula function. Finally, the probability that the responses meet the specifications simultaneously is used to obtain the optimal settings. The advantages of the proposed method lie in the consideration of multiple correlation patterns among responses, the absence of restrictions on the response distributions, and the use of nonparametric smoothing to reduce the risk of model misspecification. The results of the case study and the simulation study validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The state-space model is a powerful statistical tool to estimate linear or non-linear discrete-time dynamic systems. This model naturally leads to the estimation problem of the time-varying parameters of the discovery-time demographic version of the susceptible-infected-recovered (SIR) model that we consider. In this paper, we consider computational methods to perform Bayesian inference on state-space models for analysing time-series data. We compare the three popular Bayesian computational methods for state-space models: the adaptive Metropolis-within-Gibbs algorithm, Liu and West's algorithm and variational approximation method based on Gaussian distributions. The performances of the three methods are compared based on synthetic datasets. Furthermore, we analyse the trend of the spread of COVID-19 in South Korea to point out the limitations of existing methods and derive meaningful results. [ABSTRACT FROM AUTHOR]

This paper proposes a generalization of Markowitz model that incorporates skewness and kurtosis into the classical mean–variance allocation framework. The principal appeal of the present approach is that it provides the closed-form solution of the optimization problem. The four moments optimal portfolio is then decomposed into the sum of three portfolios: the mean–variance optimal portfolio plus two self-financing portfolios, respectively, accounting for skewness and kurtosis. Theoretical properties of the optimal solution are discussed together with the economic interpretation. Finally, an empirical exercise on real financial data shows the contribution of the two portfolios accounting for skewness and kurtosis when financial returns depart from Normal distribution. [ABSTRACT FROM AUTHOR]

Forming process control of powder bed fusion (PBF) additive manufacturing (AM) is the key to produce high-quality qualified parts. In this paper, spreading powder process and electron-beam melting (EBM) of Ti6Al4V powder were simulated based on simulation technology, and the state of powder bed powder and melting trajectory characteristics were characterized. Firstly, the particle size distribution of Ti6Al4V powder was tested, and the particle diameter of normal distribution for simulation was determined. Then, the simulation models of spreading powder and EBM model were established. Finally, based on the simulation results, the effect of processing parameters on the quality of powder laying is analyzed, and the morphology of EBM melting trajectory is characterized. [ABSTRACT FROM AUTHOR]

The first aim of the paper is to put into practice the α , β -corrected Lilliefors goodness-of-fit test for normality (LF). This modification consists in varying a formula of calculating the empirical distribution function (EDF). Values of constants α , β in the formula depend on values of sample skewness and excess kurtosis, which is recommended in order to increase the power of the LF test. Critical values are obtained with the Monte Carlo method for sample sizes n = 10 , 14 , 20 and at a significance level α = 0.05. The power of several normality tests for a wide collection of alternative distributions is calculated. Alternative distributions are divided into 12 groups according to their skewness and excess kurtosis. The second aim is to propose a similarity measure between the normal distribution and an alternative distribution. The third aim is to propose two new alternative distributions created in order to obtain the desired values of skewness and excess kurtosis. The fourth aim is to calculate the power of tests for new alternative distributions. The paper shows that values of constants α , β in the formula of calculating the EDF influences the power of the LF test. The performance of the new proposal through the analysis of real data sets is illustrated. [ABSTRACT FROM AUTHOR]

In this paper, we propose a simple and easy-to-implement Bayesian hypothesis test for the presence of an association, described by Kendall's τ coefficient, between two variables measured on at least an ordinal scale. Owing to the absence of the likelihood functions for the data, we employ the asymptotic sampling distributions of the test statistic as the working likelihoods and then specify a truncated normal prior distribution on the noncentrality parameter of the alternative hypothesis, which results in the Bayes factor available in closed form in terms of the cumulative distribution function of the standard normal distribution. Investigating the asymptotic behaviour of the Bayes factor we find the conditions of the priors so that it is consistent to whichever the hypothesis is true. Simulation studies and a real-data application are used to illustrate the effectiveness of the proposed Bayes factor. It deserves mentioning that the proposed method can be easily covered in undergraduate and graduate courses in nonparametric statistics with an emphasis on students' Bayesian thinking for data analysis. [ABSTRACT FROM AUTHOR]

In recent decades, the use of regression models with random effects has made great progress. Among these models' attractions is the flexibility to analyze correlated data. In various situations, the distribution of the response variable presents asymmetry or bimodality. In these cases, it is possible to use the normal regression with random effect at the intercept. In light of these contexts, i.e. the desire to analyze correlated data in the presence of bimodality or asymmetry, in this paper we propose a regression model with random effect at the intercept based onthe generalized inverse Gaussian distribution model with correlated data. The maximum likelihood is adopted to estimate the parameters and various simulations are performed for correlated data. A type of residuals for the new regression is proposed whose empirical distribution is close to normal. The versatility of the new regression is demonstrated by estimating the average price per hectare of bare land in 10 municipalities in the state of São Paulo (Brazil). In this context, various databases are constantly emerging, requiring flexible modeling. Thus, it is likely to be of interest to data analysts, and can make a good contribution to the statistical literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to appraise if there is any improvement subtracting the effects of outliers from existing heteroscedastic models and whether this improvement makes difference with the existing models in achieving efficiency in capturing excess kurtosis in the returns series. The study employed both existing and outlier modified autoregressive conditional heteroscedastic (ARCH), generalized autoregressive conditional heteroscedastic (GARCH), exponential GARCH (EGARCH), Glosten, Jagnnathan and Runkle GARCH (GJR-GARCH) models with respect to normal and student-t distributions to assess the portion of excess kurtosis of the returns series expressed compare to the theoretical value of kurtosis. The data applied were the share prices of Union bank of Nigeria and Unity bank from January 3, 2006 to November 24, 2016, comprising 2690 observations and were obtained from Nigerian Stock Exchange. The results obtained revealed that the Outlier Modified GARCH-type models chosen were adequate and sufficiently reducing the value of excess kurtosis in close proximity to the theoretical value. Therefore, the modification of existing GARCH-type models by subtracting the effects of outliers seems to show a substantive improvement in the portion of excess kurtosis captured and thus proves that the Outlier Modified GARCH-type models make difference with the existing ones. [ABSTRACT FROM AUTHOR]

Random numbers cover a vast spectrum of applications. Hence generating it effectively with high performance is the need of the hour. This paper presents the novel design and implementation of high performance and energy-efficient true random number generator (TRNG) using images as a source. In the proposed work, the harvesting mechanism that comprises of hashing technique block (HTB) is used to reduce the intensity of pattern, an event counting circuit (ECC) is used for comparing the events, while a linear feedback shift register (LFSR), designed by considering a primitive polynomial function, is used to obtain the random numbers. The addition of 8 × 1 multiplexer (MUX) with meta-stable circuit feeder control lines had further increased the unpredictability in the proposed system. The implementation of the work has been done in the Xilinx Vivado simulation tool followed by the Cadence Virtuoso circuit simulation environment. The maximum speed of 1.5 Gbps with power dissipation of 1 mW and 0.7 pJ/bit energy efficiency with a layout area of 2218 μm2 has been achieved in this work. NIST 800.22 statistical test suite and uniformity test comprising of Kolmogorov–Smirnov and Chi-square test have also been performed for validation of generated random numbers. The obtained binary sequences have passed all tests successfully with calculated entropy up to 0.999999999. The autocorrelation factor (ACF) of the output bit streams has been obtained as approximately zero (∼0) within 96% confidence bounds of a Gaussian distribution (µ = 0, 3σ). The proposed design is thus suitable for true random number generation. [ABSTRACT FROM AUTHOR]

Network (graph) data analysis is a popular research topic in statistics and machine learning. In application, one is frequently confronted with graph two-sample hypothesis testing where the goal is to test the difference between two graph populations. Several statistical tests have been devised for this purpose in the context of binary graphs. However, many of the practical networks are weighted and existing procedures cannot be directly applied to weighted graphs. In this paper, we study the weighted graph two-sample hypothesis testing problem and propose a practical test statistic. We prove that the proposed test statistic converges in distribution to the standard normal distribution under the null hypothesis and analyze its power theoretically. The simulation study shows that the proposed test has satisfactory performance and it substantially outperforms the existing counterpart in the binary graph case. A real data application is provided to illustrate the method. [ABSTRACT FROM AUTHOR]

This paper proposes a novel framework to address the model-vehicle mismatch (MVM) challenge of yaw stability control, which introduces the Gaussian Process-based Model Predictive Control into the classical two-layer structure. In the upper layer, the supervisor controller calculates the compensation torque required for vehicle turning. Gaussian Process regression is employed to compensate model mismatch and unmodelled dynamics. The chance constraints on sideslip angle are converted into double half-space constraints by the normal distribution quantile function. In the lower layer, the subordinate controller utilises the nonlinear slip rate model to distribute torque to the wheels in the form of braking torque. A new assignment rule of braking torque weight is proposed according to the yaw torque analysis. The stability of the two-layered learning MPC is ensured through proof and simulation. In the Simulink and Carsim co-simulation environment, the superiority of the proposed method is verified in the task of rapid double-lane change. Compared with the traditional MPC-based yaw stability controller, the proposed method has increased the stability tracking index and energy consumption index by around 13% and 8%. [ABSTRACT FROM AUTHOR]

In this paper, it is introduced a new parametric distribution to be used in multivariate lifetime data analysis as an alternative for the use of some existing multivariate parametric models as the popular multivariate normal distribution which is the most widely used model assumed in the analysis of continuous multivariate data. Although the normal multivariate distribution has univariate marginal normal probability distributions and simple interpretations for all their parameters, it may not be well fitted by many data sets, especially in survival data applications, usually considering logarithm transformed data. In many cases the use of parametric multivariate discrete models could be more appropriate for the data analysis. In this paper, it is introduced a generalization of the bivariate Basu-Dhar geometric distribution to a trivariate case applied to count data. Some properties of this trivariate geometric distribution, including its marginal probability distributions, order statistics distributions, the probability generating function and some simulation studies are presented. It is also presented some discussion on an extension of the trivariate case for the multivariate case. Classical and Bayesian inferences are presented assuming censored or uncensored observations. To illustrate the proposed methodology, two applications with real lifetime data are considered as examples. [ABSTRACT FROM AUTHOR]

Visual examination of visually recognisable substances, including microscopy, focus on targets or contaminants such as particles of animal origin, plant seeds, spore bodies of moulds, sclerotia, packaging material, microplastic and 'Besatz' (everything that differs from the norm). The two principal results are counts (numbers) and weights for macroscopic methods, or presence/absence for microscopic methods. The level of detection equals at least the size of one unit, usually with a weight exceeding 1 mg, which is in the range of parts per million (ppm). These parameters do not follow a normal distribution but Poisson (counts), lognormal (weights) or binomial (Booleans) distributions, with effect on the interpretation of validation parameters. As for other domains, examination methods for visual monitoring need to be properly validated and quality control during actual application is needed. In most cases procedures for validation of visual methods are based on principles adopted from other domains, such as chemical analysis. A series of examples from publications show inconsistent or not correct implementations of these validation procedures, which stress the need for dedicated validation procedures. Identification of legal ingredients and composition analysis in the domain of visual examination relies on the expertise of the laboratory staff, therefore validation of a method usually includes the validation of the expert. In the view of these specific circumstances, a Guidance for quality assurance and control of visual methods has been developed, which are being presented and discussed in this paper. The general framework of the Guidance is adopted from ISO standards (17023, 17043, 13528). Part 1 of the Guidance includes the general background, theory and principles. Part 2 presents the actual validation procedures with experimental designs and equations for calculating the relevant parameters, and can be used as blueprint for a SOP in a quality management system. An EURL and NRL network for physical hazards is strongly recommended. [ABSTRACT FROM AUTHOR]

We consider multitype Markov branching processes with immigration occurring at time points generated by Poisson random measures. These models find applications to study evolution of multitype cell populations in which new cells join the population according to a time-varying immigration mechanism. The focus of this paper is the supercritical case. We investigate the limiting behavior of the process for different rates of the Poisson random measures. In particular, we prove a result analogous to a strong LLN and establish limiting normal distributions. [ABSTRACT FROM AUTHOR]

In the real world, monitoring the number of transactions between nodes in many networks such as transportation, sales, financial communications, etc. is very important, from which network stakeholders can enjoy significant benefits, as well. The present paper attempts to show a significant reduction in the performance of the statistical methods in detecting network anomalies resulting from losing information due to disregarding the weights of edges in the case of modeling and monitoring weighted networks through using binary models. This paper focuses on and applies normal distribution in a real non social network because the statistical distribution of edges in most weighted networks is normal. The performance of the statistical model in the form of a case study, monitoring electronic components exchange network in a repair company, is described. Using simulation, the ability of the model in detecting network anomalies is compared with the binary model. [ABSTRACT FROM AUTHOR]

In this paper, we present a testing procedure for fractional orders of integration in the context of non-linear terms approximated by Fourier functions. The test statistic has an asymptotic standard normal distribution and several Monte Carlo experiments conducted in the paper show that it performs well in finite samples. Various applications using real life time series, such as US unemployment rates, US GNP and Purchasing Power Parity (PPP) of G7 countries are presented at the end of the paper. [ABSTRACT FROM AUTHOR]

The robust linear parameters varying systems identification method with multiple-model approach is addressed in this paper. Various noise and outliers commonly exist in practical industrial processes and have a serious impact on data-driven system identification methods. A statistic approach is proposed in the paper where the centralised asymmetric Laplace (CAL) distribution is employed to model the noise and therefore the parameters estimation algorithm based on CAL distribution is robust to the symmetric/asymmetric noise and outliers. CAL distribution is represented as the product of exponential distribution and Gaussian distribution, and therefore the parameters estimation formulas are deduced in the expectation maximisation algorithm framework. The efficacy and the robustness of the proposed algorithm are verified by a numerical example and the continuous stirred tank reactor system experiment. [ABSTRACT FROM AUTHOR]

In this paper the authors present a unique approach to teaching introductory statistics at both the undergraduate and graduate levels. The approach uses a feature in Excel called "spinners" to dynamically adjust key variables, such as sample size, confidence levels, and probabilities, among others, to enable an expanded discussion of many topics without being hampered by tedious calculations, which take up class time unnecessarily. This Excel based model eliminates dependence on internet availability, deals with multiple topics at once, and is compatible with presentation tools. In addition, the models developed by the authors are dynamic models, whereas, most online models are static. These features are not available in online applications. [ABSTRACT FROM AUTHOR]

Many extensions of the multivariate normal distribution to heavy-tailed distributions are proposed in the literature, which includes scale Gaussian mixture distribution, elliptical distribution, generalized elliptical distribution and transelliptical distribution. The inferences for each family of distributions are well studied. However, extensions are overlapped or similar to each other, and it is hard to differentiate one extension from the other. For this reason, in practice, researchers simply pick one of many extensions and apply it to the analysis. In this paper, to enlighten practitioners who should conduct statistical procedures not based on their preferences but based on how data look like, we comparatively review various extensions and their estimators. Also, we fully investigate the inclusion and exclusion relations of different extensions by Venn diagrams and examples. Moreover, in the numerical study, we illustrate visual differences of the extensions by bivariate plots and analyze different scatter matrix estimators based on the microarray data. [ABSTRACT FROM AUTHOR]