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Recurrence relations for integrals that involve the density of multivariate normal distributions are developed. These recursions allow fast computation of the moments of folded and truncated multivariate normal distributions. Besides being numerically efficient, the proposed recursions also allow us to obtain explicit expressions of low-order moments of folded and truncated multivariate normal distributions. Supplementary material for this article is available online.

Skew-symmetric families of distributions such as the skew-normal and skew-t represent supersets of the normal and t distributions, and they exhibit richer classes of extremal behaviour. By defining a non-stationary skew-normal process, which allows the easy handling of positive definite, non-stationary covariance functions, we derive a new family of max-stable processes – the extremal skew-t process. This process is a superset of non-stationary processes that include the stationary extremal-t processes. We provide the spectral representation and the resulting angular densities of the extremal skew-t process and illustrate its practical implementation.

Simulation from the truncated multivariate normal distribution in high dimensions is a recurrent problem in statistical computing and is typically only feasible by using approximate Markov chain Monte Carlo sampling. We propose a minimax tilting method for exact independently and identically distributed data simulation from the truncated multivariate normal distribution. The new methodology provides both a method for simulation and an efficient estimator to hitherto intractable Gaussian integrals. We prove that the estimator has a rare vanishing relative error asymptotic property. Numerical experiments suggest that the scheme proposed is accurate in a wide range of set-ups for which competing estimation schemes fail. We give an application to exact independently and identically distributed data simulation from the Bayesian posterior of the probit regression model.

Plane segmentation is a basic task in the automatic reconstruction of indoor and urban environments from unorganized point clouds acquired by laser scanners. As one of the most common plane-segmentation methods, standard Random Sample Consensus (RANSAC) is often used to continually detect planes one after another. However, it suffers from the spurious-plane problem when noise and outliers exist due to the uncertainty of randomly sampling the minimum subset with 3 points. An improved RANSAC method based on Normal Distribution Transformation (NDT) cells is proposed in this study to avoid spurious planes for 3D point-cloud plane segmentation. A planar NDT cell is selected as a minimal sample in each iteration to ensure the correctness of sampling on the same plane surface. The 3D NDT represents the point cloud with a set of NDT cells and models the observed points with a normal distribution within each cell. The geometric appearances of NDT cells are used to classify the NDT cells into planar and non-planar cells. The proposed method is verified on three indoor scenes. The experimental results show that the correctness exceeds 88.5% and the completeness exceeds 85.0%, which indicates that the proposed method identifies more reliable and accurate planes than standard RANSAC. It also executes faster. These results validate the suitability of the method.

Coronaviruses are enveloped RNA viruses from the Coronaviridae family affecting neurological, gastrointestinal, hepatic and respiratory systems. In late 2019 a new member of this family belonging to the Betacoronavirus genera (referred to as COVID-19) originated and spread quickly across the world calling for strict containment plans and policies. In most countries in the world, the outbreak of the disease has been serious and the number of confirmed COVID-19 cases has increased daily, while, fortunately the recovered COVID-19 cases have also increased. Clearly, forecasting the “confirmed” and “recovered” COVID-19 cases helps planning to control the disease and plan for utilization of health care resources. Time series models based on statistical methodology are useful to model time-indexed data and for forecasting. Autoregressive time series models based on two-piece scale mixture normal distributions, called TP–SMN–AR models, is a flexible family of models involving many classical symmetric/asymmetric and light/heavy tailed autoregressive models. In this paper, we use this family of models to analyze the real world time series data of confirmed and recovered COVID-19 cases.

This paper provides an introductory overview of a portion of distribution theory which is currently under intense development. The starting point of this topic has been the so-called skew-normal distribution, but the connected area is becoming increasingly broad, and its branches include now many extensions, such as the skew-elliptical families, and some forms of semiparametric formulations, extending the relevance of the field much beyond the original theme of 'skewness'. The final part of the paper illustrates connections with various areas of application, including selective sampling, models for compositional data, robust methods, some problems in econometrics, non-linear time series, especially in connection with financial data, and more.

This study introduces the Multi-objective Generalized Normal Distribution Optimization (MOGNDO) algorithm, an advancement of the Generalized Normal Distribution Optimization (GNDO) algorithm, now adapted for multi-objective optimization tasks. The GNDO algorithm, previously known for its effectiveness in single-objective optimization, has been enhanced with two key features for multi-objective optimization. The first is the addition of an archival mechanism to store non-dominated Pareto optimal solutions, ensuring a detailed record of the best outcomes. The second enhancement is a new leader selection mechanism, designed to strategically identify and select the best solutions from the archive to guide the optimization process. This enhancement positions MOGNDO as a cutting-edge solution in multi-objective optimization, setting a new benchmark for evaluating its performance against leading algorithms in the field. The algorithm's effectiveness is rigorously tested across 35 varied case studies, encompassing both mathematical and engineering challenges, and benchmarked against prominent algorithms like MOPSO, MOGWO, MOHHO, MSSA, MOALO, MOMVO, and MOAOS. Utilizing metrics such as Generational Distance (GD), Inverted Generational Distance (IGD), and Maximum Spread (MS), the study underscores MOGNDO's ability to produce Pareto fronts of high quality, marked by exceptional precision and diversity. The results affirm MOGNDO's superior performance and versatility, not only in theoretical tests but also in addressing complex real-world engineering problems, showcasing its high convergence and coverage capabilities. The source codes of the MOGNDO algorithm are publicly available at  https://nimakhodadadi.com/algorithms-%2B-codes .

Using a multisector general equilibrium model, we show that the interplay of idiosyncratic microeconomic shocks and sectoral heterogeneity results in systematic departures in the likelihood of large economic downturns relative to what is implied by the normal distribution. Such departures can emerge even though GDP fluctuations are approximately normally distributed away from the tails, highlighting the different nature of large economic downturns from regular business-cycle fluctuations. We further demonstrate the special role of input-output linkages in generating tail comovements, whereby large recessions involve not only significant GDP contractions, but also large simultaneous declines across a wide range of industries.

Labor shortage has been a severe problem in the Japanese construction industry, and the automation of construction work has been in high demand. One of the needs is the automation of soil loading onto dump trucks. This task requires pose estimation and size classification of the dump trucks to determine the appropriate loading position and volume. At actual construction sites, specifications of dump trucks are not always known in advance. However, most of the existing methods cannot robustly estimate the pose and the size of such unknown dump trucks. To address this issue, we propose a two-stage method that estimates the pose of dump trucks and then classifies their size categories. We use Normal Distribution Transform (NDT) for pose estimation of dump trucks. Specifically, we utilize NDT templates of dump trucks which distinguish global differences among size categories and simultaneously absorb local shape variations within each category. The proposed method is evaluated by data in a real-world environment. The proposed method appropriately estimates the pose of dump trucks under various settings of positions and orientations. In addition, the method correctly classifies the observed dump truck with all three predefined size categories. Furthermore, the computation time is approximately 0.13 s, which is sufficiently short for practical operation. These results indicate that the method will contribute to the automation of soil loading onto dump trucks with unknown specifications.

A new mortality model based on a mixture distribution function is proposed. We mix a half-normal distribution with a generalization of the skew-normal distribution. As a result, we get a six-parameter distribution function that has a good fit with a wide variety of mortality patterns. This mixture model is fitted to several mortality data schedules and compared with the Siler (five-parameter) and Heligman-Pollard (eight-parameter) models. Our proposal serves as a convenient compromise between the Heligman-Pollard model (which ensures a good fit with data but is often overparameterized) and the Siler model (which is more compact but fails to capture 'accident humps').