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Multivariate normal/independent (MNI) distributions contain many renowned heavy-tailed distributions such as the multivariate t , multivariate slash, multivariate contaminated normal, multivariate variance-gamma, and multivariate double exponential distributions. A frequent problem encountered in statistical analysis is the occurrence of truncated observations and non-normality such that theoretical moments are required for the estimation of the truncated multivariate normal/independent (TMNI) distributions. This paper is dedicated to deriving explicit expressions for the moments of the TMNI distributions with supports confined within a hyper-rectangle. A Monte Carlo experiment is undertaken to validate to the correctness of the proposed formulae for five selected members of the TMNI distributions. R scripts and data to reproduce the results are available in the GitHub repository. [ABSTRACT FROM AUTHOR]

• A Bayesian method is developed for the uncertainty quantification of FE models. • Expectation-Maximization strategies are combined with asymptotic approximations. • Identification uncertainty and test-to-test variability of parameters are included. • A new rationale to optimally weight the modal parameters is introduced. This paper develops a Hierarchical Bayesian Modeling (HBM) framework for uncertainty quantification of Finite Element (FE) models based on modal information. This framework uses an existing Fast Fourier Transform (FFT) approach to identify experimental modal parameters from time-history data and employs a class of maximum-entropy probability distributions to account for the mismatch between the modal parameters. It also considers a parameterized probability distribution for capturing the variability of structural parameters across multiple data sets. In this framework, the computation is addressed through Expectation-Maximization (EM) strategies, empowered by Laplace approximations. As a result, a new rationale is introduced for assigning optimal weights to the modal properties when updating structural parameters. According to this framework, the modal features' weights are equal to the inverse of the aggregate uncertainty, comprised of the identification and prediction uncertainties. The proposed framework is coherent in modeling the entire process of inferring structural parameters from response-only measurements and is comprehensive in accounting for different sources of uncertainty, including the variability of both modal and structural parameters over multiple data sets, as well as their identification uncertainties. Numerical and experimental examples are employed to demonstrate the HBM framework, wherein the environmental and operational conditions are almost constant. It is observed that the variability of parameters across data sets remains the dominant source of uncertainty while being much larger than the identification uncertainties. [ABSTRACT FROM AUTHOR]

• This paper presents a novel method to deal with correlated variables by polynomial chaos expansion. • An improved version of the fractional moment-based maximum entropy method is developed for reliability analysis. • The accuracy and efficiency of structural reliability analysis with correlated variables are enhanced. Correlated random variables are common in industry field. In reliability analysis community, Nataf transformation is considered as a powerful tool for handling correlated random variables, since it only requires the marginal probability distribution functions of input random variables. However, when accurate marginal probability distributions are unavailable, Nataf transformation cannot be used. This paper presents an alternative method for transforming correlated random variables into independent ones based on the maximum entropy principle and the polynomial chaos expansion. The proposed method only requires the first-several statistical moments of input random variables but not the probability distribution functions. Based on the proposed method for handling correlated random variables, the statistical moments of performance functions can be calculated. In order to predict the failure probability, the fractional moment-based maximum entropy method (FM-MEM) is employed due to its accuracy. However, the FM-MEM is sensitive to the initial point of its outer loop and also requires too much CPU time. Thus, an improved version is developed to enhance the performance of the algorithm. To verify the validity of the proposed method, three numerical examples and one engineering example are tested. The results show that the proposed method is a good choice for reliability analysis with correlated random variables, especially when only the statistical moment information of input random variables is available. [ABSTRACT FROM AUTHOR]

Abstract: In [A. Claesson, S. Kitaev, E. Steingrímsson, Decompositions and statistics for -trees and nonseparable permutations, Adv. in Appl. Math. 42 (2009) 313–328] we introduced an involution, h, on -trees. We neglected, however, to prove that h indeed is an involution. In this note we provide the missing proof. We also refine an equidistribution result given in the same paper. [Copyright &y& Elsevier]

Abstract: In this paper we study -statistics with side information incorporated using the method of empirical likelihood. Some basic properties of the proposed statistics are investigated. We find that by implementing the side information properly, the proposed -statistics can have smaller asymptotic variance than the existing -statistics in the literature. The proposed -statistics can achieve asymptotic efficiency in a formal sense and their weak limits admit a convolution result. We also find that the corresponding -likelihood ratio procedure, as well as the -empirical likelihood based confidence interval construction, do not benefit from incorporating side information, a result that is consistent with the result under the standard empirical likelihood ratio procedure. The impact of incorrect side information implementation in the proposed -statistics is also explored. Simulation studies are conducted to assess the finite sample performance of the proposed method. The numerical results show that with side information implemented, the deduction of asymptotic variance can be substantial in some cases, and the coverage probability of the confidence interval using the -empirical likelihood ratio based method outperforms that of the normal approximation based method, in particular in the cases when the underlying distribution is skewed. [Copyright &y& Elsevier]

Abstract: In this article we shall consider a class of strongly -periodically correlated processes with values in a separable complex Hilbert space . The periodograms of these processes and their statistical properties were previously studied by the authors. In this paper we derive the asymptotic distribution of the periodogram, that appears to be a certain Wishart distribution on . [Copyright &y& Elsevier]

Abstract: Quantization errors in discrete-cosine-transform (DCT) video compression are known as DCT residues. Knowledge on their distribution is essential in understanding rate-distortion (R-D) behaviors of generic video coding. Traditional R-D analysis adopted a simplified distortion model. Those distortion models took only quantization parameter into account. They lack adaptability to variation of video sources, as the distribution of coding errors also depends on the statistics of video source. Another common approach models the distribution of DCT residues by fitting experimental data from coded pictures to conjectured statistical distributions, but it did not provide insights into what gives rise to the distribution of DCT residues. This paper intends to quantify the distribution of DCT residues with respect to video source and with respect to the quantization strategy by understanding the quantization of DCT frequency components. Moreover, it is applied to derive an R-D model to show the advantage of the proposed distribution model. [Copyright &y& Elsevier]

Abstract: We consider a class of statistics based on -divergence for the test of independence in contingency tables. The class of statistics includes the statistics based on the power divergence as a special case. Statistic is the log likelihood ratio statistic and is Pearson''s statistic. Statistic corresponds to the statistic recommended by Cressie and Read [Multinomial goodness-of-fit tests, J. Roy. Statist. Soc. B 46 (1984) 440–464] for the goodness-of-fit test. All members of statistics have the same chi-square limiting distribution under the hypothesis of independence. In this paper, we show the derivation of an expression of approximation for the distribution of under the hypothesis of independence. The expression consists of continuous and discontinuous terms. Using the continuous term of the expression, we propose a new approximation of the distribution of . Furthermore, on the basis of the approximation, we obtain transformations that improve the speed of convergence to the chi-square limiting distribution of . As a competitor of the transformed statistic, we derive a moment-corrected-type statistic. By numerical comparison in the case of , we show that the transformed statistic performs very well. [Copyright &y& Elsevier]

Abstract: In this paper, a method to analyse a complex non-linear structure system under random excitation is proposed. First, the actual random excitation, such as earthquake, is approximated to the corresponding Gaussian process for the statistical analysis. When modelling the overall non-linear system, the overall system is divided into substructures and these are approximately transformed into modal coordinates with the random excitation. The modal equations of the overall system are expanded sequentially according to the non-linear order. Then, the perturbed equations are synthesised into the overall system and solved in a probabilistic way. Several statistical properties of a random process that are of interest in random vibration applications are reviewed in accordance with the non-linear stochastic problem. The obtained statistical properties of the non-linear random vibration are evaluated in each substructure. Comparing with the results of the numerical simulation proved the efficiency of the proposed method. [Copyright &y& Elsevier]

Cressie and Read (J. Roy. Statist. Soc. B 46 (1984) 440–464) introduced the power divergence statistics, Ra, as multinomial goodness-of-fit statistics. Each Ra has a limiting noncentral chi-square distribution under a local alternative and has a limiting normal distribution under a nonlocal alternative. Taneichi et al. (J. Multivariate Anal. 81 (2002) 335–359) derived an asymptotic approximation for the distribution of Ra under local alternatives. In this paper, using multivariate Edgeworth expansion for a continuous distribution, we show how the approximation based on the limiting normal distribution of Ra under nonlocal alternatives can be improved. We apply the expansion to the power approximation for Ra. The results of numerical investigation show that the proposed power approximation is very effective for the likelihood ratio test. [Copyright &y& Elsevier]

One form of inference found in a variety of applied areas involves classifying individuals into one of several possible populations or categories on the basis of inconclusive data. Discussed in this paper is a strategy for classification using naturally discrete data classes or data classes which are formed by discrete partitions of continuous data classes. The strategy makes use of the concept of likelihood ratio and is scale-free in the sense that, whatever their scale properties, the original measures identifying data class levels or states are not utilized. The approach is algebraically simple: no calculations of covariance or correlation are required. In addition, no distributional assumptions of any kind are required. A convergence process, applicable even when the number of data classes is small, allows ready calculation, using the normal distribution, of the probability of misclassification errors. The approach is particularly useful when data classes are conditionally independent but is also useful when this assumption is not valid, provided that there are sufficient data. Also discussed are measures of the classification or inferential value of individual data classes and of various subsets of data classes. [ABSTRACT FROM AUTHOR]