Search results for: multivariate distribution theory

Authors: Ishapathik Das, Sumen Sen, N. Rao Chaganty, Pooja Sengupta

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Dependent multivariate count data occur in several research studies. These data can be modeled by a multivariate Poisson or Negative binomial distribution constructed using copulas. However, when some of the counts are inflated, that is, the number of observations in some cells are much larger than other cells, then the copula based multivariate Poisson (or Negative binomial) distribution may not fit well and it is not an appropriate statistical model for the data. There is a need to modify or adjust the multivariate distribution to account for the inflated frequencies. In this article, we consider the situation where the frequencies of two cells are higher compared to the other cells, and develop a doubly inflated multivariate Poisson distribution function using multivariate Gaussian copula. We also discuss procedures for regression on covariates for the doubly inflated multivariate count data. For illustrating the proposed methodologies, we present a real data containing bivariate count observations with inflations in two cells. Several models and linear predictors with log link functions are considered, and we discuss maximum likelihood estimation to estimate unknown parameters of the models.

Keywords: copula, Gaussian copula, multivariate distributions, inflated distributios

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Authors: Bader Alruwaili, Surajit Ray

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Finite mixtures are a flexible and powerful tool that can be used for univariate and multivariate distributions, and a wide range of research analysis has been conducted based on the multivariate normal mixture and multivariate of a t-mixture. Determining the number of modes is an important activity that, in turn, allows one to determine the number of homogeneous groups in a population. Our work currently being carried out relates to the study of the modality of the skew normal distribution in the univariate and multivariate cases. For the skew normal distribution, the aims are associated with studying the modality of the skew normal distribution and providing the ridgeline, the ridgeline elevation function, the $\Pi$ function, and the curvature function, and this will be conducive to an exploration of the number and location of mode when mixing the two components of skew normal distribution. The subsequent objective is to apply these results to the application of real world data sets, such as flow cytometry data.

Keywords: mode, modality, multivariate skew normal, finite mixture, number of mode

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Authors: Betty Johanna Garzon Rozo, Jonathan Crook, Fernando Moreira

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Operational risk losses are heavy tailed and are likely to be asymmetric and extremely dependent among business lines/event types. We propose a new methodology to assess, in a multivariate way, the asymmetry and extreme dependence between severity distributions, and to calculate the capital for Operational Risk. This methodology simultaneously uses (i) several parametric distributions and an alternative mix distribution (the Lognormal for the body of losses and the Generalized Pareto Distribution for the tail) via extreme value theory using SAS®, (ii) the multivariate skew t-copula applied for the first time for operational losses and (iii) Bayesian theory to estimate new n-dimensional skew t-copula models via Markov chain Monte Carlo (MCMC) simulation. This paper analyses a newly operational loss data set, SAS Global Operational Risk Data [SAS OpRisk], to model operational risk at international financial institutions. All the severity models are constructed in SAS® 9.2. We implement the procedure PROC SEVERITY and PROC NLMIXED. This paper focuses in describing this implementation.

Keywords: operational risk, loss distribution approach, extreme value theory, copulas

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Authors: Malay Bhattacharyya, Saparya Suresh

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The Correlation Structure associated with a portfolio is subjected to vary across time. Studying the structural breaks in the time-dependent Correlation matrix associated with a collection had been a subject of interest for a better understanding of the market movements, portfolio selection, etc. The current paper proposes a methodology for testing the change in the time-dependent correlation structure of a portfolio in the high dimensional data using the techniques of generalized inverse, singular valued decomposition and multivariate distribution theory which has not been addressed so far. The asymptotic properties of the proposed test are derived. Also, the performance and the validity of the method is tested on a real data set. The proposed test performs well for detecting the change in the dependence of global markets in the context of high dimensional data.

Keywords: correlation structure, high dimensional data, multivariate distribution theory, singular valued decomposition

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Authors: Edokpa Idemudia Waziri, Salisu S. Umar

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The Hotellng’s T^2 is a well-known statistic for detecting a shift in the mean vector of a multivariate normal distribution. Control charts based on T have been widely used in statistical process control for monitoring a multivariate process. Although it is a powerful tool, the T statistic is deficient when the shift to be detected in the mean vector of a multivariate process is small and consistent. The Multivariate Exponentially Weighted Moving Average (MEWMA) control chart is one of the control statistics used to overcome the drawback of the Hotellng’s T statistic. In this paper, the probability distribution of the Average Run Length (ARL) of the MEWMA control chart when the quality characteristics exhibit substantial cross correlation and when the process is in-control and out-of-control was derived using the Markov Chain algorithm. The derivation of the probability functions and the moments of the run length distribution were also obtained and they were consistent with some existing results for the in-control and out-of-control situation. By simulation process, the procedure identified a class of ARL for the MEWMA control when the process is in-control and out-of-control. From our study, it was observed that the MEWMA scheme is quite adequate for detecting a small shift and a good way to improve the quality of goods and services in a multivariate situation. It was also observed that as the in-control average run length ARL0¬ or the number of variables (p) increases, the optimum value of the ARL0pt increases asymptotically and as the magnitude of the shift σ increases, the optimal ARLopt decreases. Finally, we use the example from the literature to illustrate our method and demonstrate its efficiency.

Keywords: average run length, markov chain, multivariate exponentially weighted moving average, optimal smoothing parameter

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Authors: Chia-Hau Liu, Tai-Yue Wang

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Traditional multivariate control charts assume that measurement from manufacturing processes follows a multivariate normal distribution. However, this assumption may not hold or may be difficult to verify because not all the measurement from manufacturing processes are normal distributed in practice. This study develops a new multivariate control chart for monitoring the processes with non-normal data. We propose a mechanism based on integrating the one-class classification method and the adaptive technique. The adaptive technique is used to improve the sensitivity to small shift on one-class classification in statistical process control. In addition, this design provides an easy way to allocate the value of type I error so it is easier to be implemented. Finally, the simulation study and the real data from industry are used to demonstrate the effectiveness of the propose control charts.

Keywords: multivariate control chart, statistical process control, one-class classification method, non-normal data

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Authors: Serge Provost, Abdous Saboor

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A q-analogue of the generalized extreme value distribution which includes the Gumbel distribution is introduced. The additional parameter q allows for increased modeling flexibility. The resulting distribution can have a finite, semi-infinite or infinite support. It can also produce several types of hazard rate functions. The model parameters are determined by making use of the method of maximum likelihood. It will be shown that it compares favourably to three related distributions in connection with the modeling of a certain hydrological data set.

Keywords: extreme value theory, generalized extreme value distribution, goodness-of-fit statistics, Gumbel distribution

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Authors: Behrooz Khalilloo, Hamid Shahriari, Emad Roghanian

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Process capability indices (PCIs) are important concepts of statistical quality control and measure the capability of processes and how much processes are meeting certain specifications. An important issue in statistical quality control is parameter estimation. Under the assumption of multivariate normality, the distribution parameters, mean vector and variance-covariance matrix must be estimated, when they are unknown. Classic estimation methods like method of moment estimation (MME) or maximum likelihood estimation (MLE) makes good estimation of the population parameters when data are not contaminated. But when outliers exist in the data, MME and MLE make weak estimators of the population parameters. So we need some estimators which have good estimation in the presence of outliers. In this work robust M-estimators for estimating these parameters are used and based on robust parameter estimators, robust process capability indices are introduced. The performances of these robust estimators in the presence of outliers and their effects on process capability indices are evaluated by real and simulated multivariate data. The results indicate that the proposed robust capability indices perform much better than the existing process capability indices.

Keywords: multivariate process capability indices, robust M-estimator, outlier, multivariate quality control, statistical quality control

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Authors: Shumaila Ehtisham

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In Statistical Distribution Theory, considering an additional parameter to classical distributions is a usual practice. In this study, a new distribution referred to as α-Power Pareto distribution is introduced by including an extra parameter. Several properties of the proposed distribution including explicit expressions for the moment generating function, mode, quantiles, entropies and order statistics are obtained. Unknown parameters have been estimated by using maximum likelihood estimation technique. Two real datasets have been considered to examine the usefulness of the proposed distribution. It has been observed that α-Power Pareto distribution outperforms while compared to different variants of Pareto distribution on the basis of model selection criteria.

Keywords: α-power transformation, maximum likelihood estimation, moment generating function, Pareto distribution

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Authors: I. M. L. Nadeesha Jayaweera, Adao Alex Trindade

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In choosing a candidate model in likelihood-based modeling via an information criterion, the practitioner is often faced with the difficult task of deciding just how far up the ranked list to look. Motivated by this pragmatic necessity, we construct an uncertainty band for a generalized (model selection) information criterion (GIC), defined as a criterion for which the limit in probability is identical to that of the normalized log-likelihood. This includes common special cases such as AIC & BIC. The method starts from the asymptotic normality of the GIC for the joint distribution of the candidate models in an independent and identically distributed (IID) data framework and proceeds by deriving the (asymptotically) exact distribution of the minimum. The calculation of an upper quantile for its distribution then involves the computation of multivariate Gaussian integrals, which is amenable to efficient implementation via the R package "mvtnorm". The performance of the methodology is tested on simulated data by checking the coverage probability of nominal upper quantiles and compared to the bootstrap. Both methods give coverages close to nominal for large samples, but the bootstrap is two orders of magnitude slower. The methodology is subsequently extended to two other commonly used model structures: regression and time series. In the regression case, we derive the corresponding asymptotically exact distribution of the minimum GIC invoking Lindeberg-Feller type conditions for triangular arrays and are thus able to similarly calculate upper quantiles for its distribution via multivariate Gaussian integration. The bootstrap once again provides a default competing procedure, and we find that similar comparison performance metrics hold as for the IID case. The time series case is complicated by far more intricate asymptotic regime for the joint distribution of the model GIC statistics. Under a Gaussian likelihood, the default in most packages, one needs to derive the limiting distribution of a normalized quadratic form for a realization from a stationary series. Under conditions on the process satisfied by ARMA models, a multivariate normal limit is once again achieved. The bootstrap can, however, be employed for its computation, whence we are once again in the multivariate Gaussian integration paradigm for upper quantile evaluation. Comparisons of this bootstrap-aided semi-exact method with the full-blown bootstrap once again reveal a similar performance but faster computation speeds. One of the most difficult problems in contemporary statistical methodological research is to be able to account for the extra variability introduced by model selection uncertainty, the so-called post-model selection inference (PMSI). We explore ways in which the GIC uncertainty band can be inverted to make inferences on the parameters. This is being attempted in the IID case by pivoting the CDF of the asymptotically exact distribution of the minimum GIC. For inference one parameter at a time and a small number of candidate models, this works well, whence the attained PMSI confidence intervals are wider than the MLE-based Wald, as expected.

Keywords: model selection inference, generalized information criteria, post model selection, Asymptotic Theory

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Authors: Mokhtar Bouazza

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In this paper, the simplified theory will be used to predict the thermoelastic buckling behavior of rectangular functionally graded plates. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. The simplified theory is used to obtain the buckling of the plate under different types of thermal loads. The thermal loads are assumed to be uniform, linear, and non-linear distribution through the thickness. Additional numerical results are presented for FGM plates that show the effects of various parameters on thermal buckling response.

Keywords: buckling, functionally graded, plate, simplified higher-order deformation theory, thermal loading

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Authors: Longqing Li

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The paper addresses the inefficiency of the classical model in measuring the Value-at-Risk (VaR) using a normal distribution or a Student’s t distribution. Specifically, the paper focuses on the one day ahead Value-at-Risk (VaR) of major stock market’s daily returns in US, UK, China and Hong Kong in the most recent ten years under 95% confidence level. To improve the predictable power and search for the best performing model, the paper proposes using two leading alternatives, Extreme Value Theory (EVT) and a family of GARCH models, and compares the relative performance. The main contribution could be summarized in two aspects. First, the paper extends the GARCH family model by incorporating EGARCH and TGARCH to shed light on the difference between each in estimating one day ahead Value-at-Risk (VaR). Second, to account for the non-normality in the distribution of financial markets, the paper applies Generalized Error Distribution (GED), instead of the normal distribution, to govern the innovation term. A dynamic back-testing procedure is employed to assess the performance of each model, a family of GARCH and the conditional EVT. The conclusion is that Exponential GARCH yields the best estimate in out-of-sample one day ahead Value-at-Risk (VaR) forecasting. Moreover, the discrepancy of performance between the GARCH and the conditional EVT is indistinguishable.

Keywords: Value-at-Risk, Extreme Value Theory, conditional EVT, backtesting

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Authors: J. J. Vargas, N. Prieto, L. A. Toro

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Control charts are commonly used to monitor processes involving either variable or attribute of quality characteristics and determining the control limits as a critical task for quality engineers to improve the processes. Nonetheless, in some applications it is necessary to include an estimation of efficiency. In this paper, the ability to define the efficiency of an industrial process was added to a control chart by means of incorporating a data envelopment analysis (DEA) approach. In depth, a Bayesian estimation was performed to calculate the posterior probability distribution of parameters as means and variance and covariance matrix. This technique allows to analyse the data set without the need of using the hypothetical large sample implied in the problem and to be treated as an approximation to the finite sample distribution. A rejection simulation method was carried out to generate random variables from the parameter functions. Each resulting vector was used by stochastic DEA model during several cycles for establishing the distribution of each efficiency measures for each DMU (decision making units). A control limit was calculated with model obtained and if a condition of a low level efficiency of DMU is presented, system efficiency is out of control. In the efficiency calculated a global optimum was reached, which ensures model reliability.

Keywords: data envelopment analysis, DEA, Multivariate control chart, rejection simulation method

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Authors: Qiao Fan, Xiaobo Guo, Junxian Zhu, Xiaohu Ding, Ching-Yu Cheng, Tien-Yin Wong, Mingguang He, Heping Zhang, Xueqin Wang

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A systematic, simultaneous analysis of multiple phenotypes in genome-wide association studies (GWASs) draws a great attention to integrate the signals from single phenotypes with increased power. However, lacking an interpretable and efficient multivariate GWAS analysis impede the application of such approach. In this study, we propose to decompose the multivariate model into a series of simple univariate models. This transformation illuminates what exactly the individual trait contributes to the significant signals from the multivariate analyses. By employing our approach in the analysis of three myopia-related endophenotypes from the Singapore Malay Eye Study (SIMES), we identify novel candidate loci which were successfully validated in an independent Guangzhou Twin Eye Study (GTES).

Keywords: GWAS multivariate, multiple traits, myopia, association

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Authors: Randa Ismail Sharafeddine

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The Islamic economic system is distinctive in that it implicitly recognizes money as a separate, independent component of production capable of assuming risk and so entitled to the same reward as other Entrepreneurial Factors of Production (EFP). Conventional theory does not identify money capital explicitly as a component of production; rather, interest is recognized as a reward for capital, the interest rate is the cost of money capital, and it is also seen as a cost of physical capital. The conventional theory of production examines how diverse non-entrepreneurial resources (Land, Labor, and Capital) are selected; however, the economic theory community is largely unaware of the reasons why these resources choose to remain as non-entrepreneurial resources as opposed to becoming entrepreneurial resources. Should land, labor, and financial asset owners choose to work for others in return for rent, income, or interest, or should they engage in entrepreneurial risk-taking in order to profit. This is a decision made often in the actual world, but it has never been effectively treated in economic theory. This article will conduct a critical analysis of the conventional classification of factors of production and propose a classification for resource allocation and income distribution (Rent, Wages, Interest, and Profits) that is more rational, even within the conventional theoretical framework for evaluating and developing production and distribution theories. Money is an essential component of production in an Islamic economy, and it must be used to sustain economic activity.

Keywords: financial capital, production theory, distribution theory, economic activity, riba avoidance, institution of participation

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Authors: Carlos Gonzales, Zaida Quiroz, Marcos Prates

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Several spatial variables collected at the same location that share a common spatial distribution can be modeled simultaneously through a multivariate geostatistical model that takes into account the correlation between these variables and the spatial autocorrelation. The main goal of this model is to perform spatial prediction of these variables in the region of study. Here we focus on a geostatistical multivariate formulation that relies on sharing common spatial random effect terms. In particular, the first response variable can be modeled by a mean that incorporates a shared random spatial effect, while the other response variables depend on this shared spatial term, in addition to specific random spatial effects. Each spatial random effect is defined through a Gaussian process with a valid covariance function, but in order to improve the computational efficiency when the data are large, each Gaussian process is approximated to a Gaussian random Markov field (GRMF), specifically to the block nearest neighbor Gaussian process (Block-NNGP). This approach involves dividing the spatial domain into several dependent blocks under certain constraints, where the cross blocks allow capturing the spatial dependence on a large scale, while each individual block captures the spatial dependence on a smaller scale. The multivariate geostatistical model belongs to the class of Latent Gaussian Models; thus, to achieve fast Bayesian inference, it is used the integrated nested Laplace approximation (INLA) method. The good performance of the proposed model is shown through simulations and applications for massive data.

Keywords: Block-NNGP, geostatistics, gaussian process, GRMF, INLA, multivariate models.

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Authors: Eva L. Sanjuán, Jacinto Martín, M. Isabel Parra, Mario M. Pizarro

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In Extreme Value Theory, inference estimation for the parameters of the distribution is made employing a small part of the observation values. When block maxima values are taken, many data are discarded. We developed a new Bayesian inference model to seize all the information provided by the data, introducing informative priors and using the relations between baseline and limit parameters. Firstly, we studied the accuracy of the new model for three baseline distributions that lead to a Gumbel extreme distribution: Exponential, Normal and Gumbel. Secondly, we considered mixtures of Normal variables, to simulate practical situations when data do not adjust to pure distributions, because of perturbations (noise).

Keywords: bayesian inference, extreme value theory, Gumbel distribution, highly informative prior

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Authors: Juan Francisco Reinoso Gordo, Francisco Javier Ariza-López, José Rodríguez Avi, Domingo Barrera Rosillo

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The evaluation of the quality of a data product is based on the comparison of the product with a reference of greater accuracy. In the case of MDE data products, quality assessment usually focuses on positional accuracy and few studies consider other terrain characteristics, such as slope and orientation. The proposal that is made consists of evaluating the similarity of two DEMs (a product and a reference), through the joint analysis of the distribution functions of the variables of interest, for example, elevations, slopes and orientations. This is a multivariable approach that focuses on distribution functions, not on single parameters such as mean values or dispersions (e.g. root mean squared error or variance). This is considered to be a more holistic approach. The use of the Kolmogorov-Smirnov test is proposed due to its non-parametric nature, since the distributions of the variables of interest cannot always be adequately modeled by parametric models (e.g. the Normal distribution model). In addition, its application to the multivariate case is carried out jointly by means of a single test on the convolution of the distribution functions of the variables considered, which avoids the use of corrections such as Bonferroni when several statistics hypothesis tests are carried out together. In this work, two DEM products have been considered, DEM02 with a resolution of 2x2 meters and DEM05 with a resolution of 5x5 meters, both generated by the National Geographic Institute of Spain. DEM02 is considered as the reference and DEM05 as the product to be evaluated. In addition, the slope and aspect derived models have been calculated by GIS operations on the two DEM datasets. Through sample simulation processes, the adequate behavior of the Kolmogorov-Smirnov statistical test has been verified when the null hypothesis is true, which allows calibrating the value of the statistic for the desired significance value (e.g. 5%). Once the process has been calibrated, the same process can be applied to compare the similarity of different DEM data sets (e.g. the DEM05 versus the DEM02). In summary, an innovative alternative for the comparison of DEM data sets based on a multinomial non-parametric perspective has been proposed by means of a single Kolmogorov-Smirnov test. This new approach could be extended to other DEM features of interest (e.g. curvature, etc.) and to more than three variables

Keywords: data quality, DEM, kolmogorov-smirnov test, multivariate DEM comparison

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Authors: Yuyang Cheng, Marcos Escobar-Anel

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This paper introduces a multivariate 4/2 stochastic covariance process generalizing the one-dimensional counterparts presented in Grasselli (2017). Our construction permits stochastic correlation not only among stocks but also among volatilities, also known as co-volatility movements, both driven by more convenient 4/2 stochastic structures. The parametrization is flexible enough to separate these types of correlation, permitting their individual study. Conditions for proper changes of measure and closed-form characteristic functions under risk-neutral and historical measures are provided, allowing for applications of the model to risk management and derivative pricing. We apply the model to an expected utility theory problem in incomplete markets. Our analysis leads to closed-form solutions for the optimal allocation and value function. Conditions are provided for well-defined solutions together with a verification theorem. Our numerical analysis highlights and separates the impact of key statistics on equity portfolio decisions, in particular, volatility, correlation, and co-volatility movements, with the latter being the least important in an incomplete market.

Keywords: stochastic covariance process, 4/2 stochastic volatility model, stochastic co-volatility movements, characteristic function, expected utility theory, verication theorem

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Authors: Emmanuel Iyamuremye

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Extreme rainfall events have caused significant damage to agriculture, ecology, and infrastructure, disruption of human activities, injury, and loss of life. They also have significant social, economic, and environmental consequences because they considerably damage urban as well as rural areas. Early detection of extreme maximum rainfall helps to implement strategies and measures, before they occur, hence mitigating the consequences. Extreme value theory has been used widely in modeling extreme rainfall and in various disciplines, such as financial markets, the insurance industry, failure cases. Climatic extremes have been analyzed by using either generalized extreme value (GEV) or generalized Pareto (GP) distributions, which provides evidence of the importance of modeling extreme rainfall from different regions of the world. In this paper, we focused on Peak Over Thresholds approach, where the Poisson-generalized Pareto distribution is considered as the proper distribution for the study of the exceedances. This research also considers the use of the generalized Pareto (GP) distribution with a Poisson model for arrivals to describe peaks over a threshold. The research used statistical techniques to fit models that used to predict extreme rainfall in Kigali. The results indicate that the proposed Poisson-GP distribution provides a better fit to maximum monthly rainfall data. Further, the Poisson-GP models are able to estimate various return levels. The research also found a slow increase in return levels for maximum monthly rainfall for higher return periods, and further, the intervals are increasingly wider as the return period is increasing.

Keywords: exceedances, extreme value theory, generalized Pareto distribution, Poisson generalized Pareto distribution

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Authors: Chimezie P. Nnanwa, Thomas C. Urama, Patrick O. Ezepue

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In this paper we use Random Matrix Theory to analyze the eigen-structure of the empirical correlations of 82 stocks which are consistently traded in the Nigerian Stock Exchange (NSE) over a 4-year study period 3 August 2009 to 26 August 2013. We apply the Marchenko-Pastur distribution of eigenvalues of a purely random matrix to investigate the presence of investment-pertinent information contained in the empirical correlation matrix of the selected stocks. We use hypothesised standard normal distribution of eigenvector components from RMT to assess deviations of the empirical eigenvectors to this distribution for different eigenvalues. We also use the Inverse Participation Ratio to measure the deviation of eigenvectors of the empirical correlation matrix from RMT results. These preliminary results on the dynamics of asset price correlations in the NSE are important for improving risk-return trade-offs associated with Markowitz’s portfolio optimization in the stock exchange, which is pursued in future work.

Keywords: correlation matrix, eigenvalue and eigenvector, inverse participation ratio, portfolio optimization, random matrix theory

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Authors: Asmaa M. Hussein, Amr Wassal, Ahmed Farouk Al-Sadek, A. F. Abd El-Rahman

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In this study, a multivariate analysis of potato spectroscopic data was presented to detect the presence of brown rot disease or not. Near-Infrared (NIR) spectroscopy (1,350-2,500 nm) combined with multivariate analysis was used as a rapid, non-destructive technique for the detection of brown rot disease in potatoes. Spectral measurements were performed in 565 samples, which were chosen randomly at the infection place in the potato slice. In this study, 254 infected and 311 uninfected (brown rot-free) samples were analyzed using different advanced statistical analysis techniques. The discrimination performance of different multivariate analysis techniques, including classification, pre-processing, and dimension reduction, were compared. Applying a random forest algorithm classifier with different pre-processing techniques to raw spectra had the best performance as the total classification accuracy of 98.7% was achieved in discriminating infected potatoes from control.

Keywords: Brown rot disease, NIR spectroscopy, potato, random forest

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Authors: Tianhao Zhang, Cen Chen, Dawei Cheng, Yuqi Liang, Yuanyuan Liang

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Dealing with anomalies is a crucial preprocessing step for multivariate time series prediction. However, existing methods that separate anomaly preprocessing and model training into two stages have certain limitations. Specifically, these methods fail to leverage auxiliary information necessary to distinguish latent anomalies related to spatiotemporal factors during the preprocessing stage. Instead, they solely rely on data distribution for detection which may lead to incorrect processing of many samples that are beneficial for training. To address this, we propose STTS-EAD, an end-to-end method that seamlessly integrates anomaly detection into the training process of multivariate time series forecasting and aims to improve Spatio-Temporal learning based Time Series prediction via Embedded Anomaly Detection. Our proposed STTS-EAD leverages spatio-temporal information for forecasting and anomaly detection, with the two parts alternately executed and optimized for each other. To the best of our knowledge, STTS-EAD is the first to integrate anomaly detection and forecasting tasks in the training phase for improving the accuracy of multivariate time series forecasting. Extensive experiments on a public stock dataset and two real-world sales datasets from a renowned coffee chain enterprise show that our proposed method can effectively process detected anomalies in the training stage to improve forecasting performance in the inference stage and significantly outperform baselines.

Keywords: multivariate time series, anomaly detection, time series forecasting, spatiotemporal feature learning

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Authors: Nagarjuna Remalli, Robert Brandt

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Down-sizing of combustion engines in automobiles are prevailed owing to required increase in efficiency. This leads to a stress increment on valve springs, which affects their intended function due to an increase in relaxation. High strength martensitic steels are used for valve spring applications. Recent investigations unveiled that low temperature creep (LTC) in martensitic steels obey a logarithmic creep law. The exhaustion theory links the logarithmic creep behavior to an activation energy which is characteristic for any given time during creep. This activation energy increases with creep strain due to barriers of low activation energies exhausted during creep. The assumption of the exhaustion theory is that the material is inhomogeneous in microscopic scale. According to these assumptions it is anticipated that small obstacles (e. g. ε–carbides) having a wide range of size distribution are non-uniformly distributed in the materials. X-ray diffraction studies revealed the presence of ε–carbides in high strength martensitic steels. In this study, high strength martensitic steels that are crept in the temperature range of 75 – 150 °C were investigated with the aid of a transmission electron microscope for the evidence of an inhomogeneous distribution of obstacles having different size to examine the validation of exhaustion theory.

Keywords: creep mechanisms, exhaustion theory, low temperature creep, martensitic steels

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Authors: Azadeh Golshan, Craig Evans, Phillip Geary, Abigail Morrow, Zoe Rogers, Marcel Maeder

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22 physicochemical variables have been determined in water samples collected weekly from January to December in 2013 from three sampling stations located within a major drinking water reservoir. Classical Multivariate Curve Resolution Alternating Least Squares (MCR-ALS) analysis was used to investigate the environmental factors associated with the physico-chemical variability of the water samples at each of the sampling stations. Matrix augmentation MCR-ALS (MA-MCR-ALS) was also applied, and the two sets of results were compared for interpretative clarity. Links between these factors, reservoir inflows and catchment land-uses were investigated and interpreted in relation to chemical composition of the water and their resolved geographical distribution profiles. The results suggested that the major factors affecting reservoir water quality were those associated with agricultural runoff, with evidence of influence on algal photosynthesis within the water column. Water quality variability within the reservoir was also found to be strongly linked to physical parameters such as water temperature and the occurrence of thermal stratification. The two methods applied (MCR-ALS and MA-MCR-ALS) led to similar conclusions; however, MA-MCR-ALS appeared to provide results more amenable to interpretation of temporal and geological variation than those obtained through classical MCR-ALS.

Keywords: drinking water reservoir, multivariate analysis, physico-chemical parameters, water quality

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Authors: M. T. Alodat

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In this paper, we propose a mechanism for skewing any symmetric distribution. The new distribution is called the deflation-inflation distribution (DID). We discuss some statistical properties of the DID such moments, stochastic representation, log-concavity. Also we fit the distribution to real data and we compare it to normal distribution and Azzlaini's skew normal distribution. Numerical results show that the DID fits the the tree ring data better than the other two distributions.

Keywords: normal distribution, moments, Fisher information, symmetric distributions

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Authors: Jeffrey Tzu-Hao Tsai, Yi-Shan Wong

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This article proposes a cohort-age-period (CAP) model to characterize multi-population mortality processes using cohort, age, and period variables. Distinct from the factor-based Lee-Carter-type decomposition mortality model, this approach is empirically based and includes the age, period, and cohort variables into the equation system. The model not only provides a fruitful intuition for explaining multivariate mortality change rates but also has a better performance in forecasting future patterns. Using the US and the UK mortality data and performing ten-year out-of-sample tests, our approach shows smaller mean square errors in both countries compared to the models in the literature.

Keywords: longevity risk, stochastic mortality model, multivariate mortality rate, risk management

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Authors: Boukhris Lahouari, Bouchetara Mostefa

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The active safety of a vehicle is mainly influenced by the properties of the installed braking system. With the increase in road traffic density and travel speeds, increasingly stringent requirements are placed on the vehicle's behaviour during braking. The achievable decelerations are limited by the physical aspect characterized by the coefficient of friction between the tires and the ground. As a result, it follows that an optimized distribution of braking forces becomes necessary for a better use of friction coefficients. This objective could only be achieved if sufficient knowledge is available on the theory of vehicle dynamics during braking and on current standards for the approval of braking systems. These will facilitate the development of a braking force calculation algorithm that will enable an optimized distribution of braking forces to be achieved. Operating safety is conditioned by the requirements of efficiency, progressiveness, regularity or fidelity of a braking system without obviously neglecting the recommendations imposed by the legislator.

Keywords: brake force distribution, distribution diagram, friction coefficient, brake by wire

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Authors: Abilio Pires Zacarias

Abstract:

Analyzing company boards of directors is a relevant and timely topic. As the representative of shareholders, the board is the most senior management body of this type of company. Therefore, ascertaining the best kind of candidates to nominate, namely the most appropriate characteristics for leading the board to achieve better levels of performance, is certainly of great interest. The companies selected for this study were the 1,000 largest non-financial companies and the 100 largest financial companies in Portugal according to the Instituto Nacional de Estatística for 2010. The information stemmed from a questionnaire addressed to the person in charge of daily company management and then processed through STATA 17 with the multivariate analysis of variables - MANOVA. The study may correspondingly report that the vast majority of boards in the sample operate a dual leadership structure. By in terms of its prevalence, unitary leadership represents only a minority. Agency theory and stewardship theory postulate different characteristics for the ideal chairman but neither receive confirmation from our results. On the other hand, our findings do validate the behavioral theory of firms (BToF), concluding that experience is associated with organizational performance. This study is also relevant due to its analysis of companies not listed on the financial markets not only because of their weighting in the economy but also because they remain only very poorly studied in this field and thus also correspondingly contributing to deepening the literature.

Keywords: agency theory, behavioral theory of the firm, board of directors, corporate governance, stewardship theory

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Authors: Faisal G. Khamis, Ghaleb A. El-Refae

Abstract:

Many researchers have studied socioeconomic, health, and security variables in the developed countries; however, very few studies used multivariate analysis in developing countries. The current study contributes to the scarce literature about the determinants of the variance in socioeconomic, health, and security factors. Questions raised were whether the independent variables (IVs) of governorate and year impact the socioeconomic, health, and security dependent variables (DVs) in Jordan, whether the marginal mean of each DV in each governorate and in each year is significant, which governorates are similar in difference means of each DV, and whether these DVs vary. The main objectives were to determine the source of variances in DVs, collectively and separately, testing which governorates are similar and which diverge for each DV. The research design was time series and cross-sectional analysis. The main hypotheses are that IVs affect DVs collectively and separately. Multivariate and univariate analyses of variance were carried out to test these hypotheses. The population of 12 governorates in Jordan and the available data of 15 years (2000–2015) accrued from several Jordanian statistical yearbooks. We investigated the effect of two factors of governorate and year on the four DVs of divorce rate, mortality rate, unemployment percentage, and crime rate. All DVs were transformed to multivariate normal distribution. We calculated descriptive statistics for each DV. Based on the multivariate analysis of variance, we found a significant effect in IVs on DVs with p < .001. Based on the univariate analysis, we found a significant effect of IVs on each DV with p < .001, except the effect of the year factor on unemployment was not significant with p = .642. The grand and marginal means of each DV in each governorate and each year were significant based on a 95% confidence interval. Most governorates are not similar in DVs with p < .001. We concluded that the two factors produce significant effects on DVs, collectively and separately. Based on these findings, the government can distribute its financial and physical resources to governorates more efficiently. By identifying the sources of variance that contribute to the variation in DVs, insights can help inform focused variation prevention efforts.

Keywords: ANOVA, crime, divorce, governorate, hypothesis test, Jordan, MANOVA, means, mortality, unemployment, year

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