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There exist many bivariate parametric copulas to model bivariate data with different dependence features. We propose a new bivariate parametric copula family that cannot only handle various dependence patterns that appear in the existing parametric bivariate copula families, but also provides a more enriched dependence structure. The proposed copula construction exploits finite mixtures of bivariate normal distributions. The mixing operation, the distinct correlation and mean parameters at each mixture component introduce quite a flexible dependence. The new parametric copula is theoretically investigated, compared with a set of classical bivariate parametric copulas and illustrated on two empirical examples from astrophysics and agriculture where some of the variables have peculiar and asymmetric dependence, respectively.

For estimating bivariate survival function under random censor- ship, it is commonly believed that the Dabrowska estimator is among the best ones while the Volterra estimator is far from being computational ef- ficiency. As we will see, the Volterra estimator is a natural extension of the Kaplan-Meier estimator to bivariate data setting. We believe that the computational 'inefficiency' of the Volterra estimator is largely due to the formidable computational complexity of the traditional recursion method. In this paper, we show by numerical study as well as theoretical analysis that the Volterra estimator, once computed by dynamic programming technique, is more computationally efficient than the Dabrowska estimator. Therefore, the Volterra estimator with dynamic programming would be quite recom- mendable in applications owing to its significant computational advantages.

Tinh Tuc town, Cao Bang province, Vietnam is prone to landslides due to the complexity of its climatic, geological, and geomorphological conditions. In this study, in order to produce a landslide susceptibility map, the modified analytical hierarchy process and landslide susceptibility analysis methods were used together with the layers, including: landslide inventory, slope, weathering crust, water storage, geology, land use, and distance from the road. In the study area, 98% of landslides occurred in highly or completely weathered units. Geology, land use, and water storage data layers were found to be important factors that are closely related with the occurrence of landslides. Although the weight of the “distance from the road” factor has a low value, the weight of layer “

This paper extends the analysis of the bivariate Seemingly Unrelated (SUR) Tobit by modeling its nonlinear dependence structure through copula and assuming non-normal marginal error distributions. For model estimation, the use of copula methods enables the use of the (classical) Inference Function for Margins (IFM) method by Joe and Xu (1996), which is more computationally attractive (feasible) than the full maximum likelihood approach. However, our simulation study shows that the IFM method provides a biased estimate of the copula parameter in the presence of censored observations in both margins. In order to obtain an unbiased estimate of the copula association parameter, we propose/develop a modified version of the IFM method, which we refer to as Inference Function for Augmented Margins (IFAM). Since the usual asymptotic approach, that is the computation of the asymptotic covariance matrix of the parameter estimates, is troublesome, we propose the use of resampling procedures (bootstrap methods) to obtain confidence intervals for the copula-based SUR Tobit model parameters. The satisfactory results from the simulation and empirical studies indicate the adequate performance of our proposed model and methods. We illustrate our procedure using bivariate data on consumption of salad dressings and lettuce by U.S. individuals.

High-accuracy flood susceptibility maps play a crucial role in flood vulnerability assessment and risk mitigation. This study assesses the potential application of three new ensemble models, which ...

In this paper we include dependency structures for electricity price forecasting and forecasting evaluation. We work with off-peak and peak time series from the German-Austrian day-ahead price, hence we analyze bivariate data. We first estimate the mean of the two time series, and then in a second step we estimate the residuals. The mean equation is estimated by OLS and elastic net and the residuals are estimated by maximum likelihood. Our contribution is to include a bivariate jump component on a mean reverting jump diffusion model in the residuals. The models' forecasts are evaluated using four different criteria, including the energy score to measure whether the correlation structure between the time series is properly included or not. In the results it is observed that the models with bivariate jumps provide better results with the energy score, which means that it is important to consider this structure in order to properly forecast correlated time series., 30 pages, 11 figures, 3 tables and Accepted in International Journal of Forecasting

Implementation of health promotion needs to be addressed is the selection of media y ang accordance with the target. Health promotion media is a tool used to help the health promotion process. The right media make information more easily accepted by the target, so that behavior will also change according to the knowledge gained. The purpose of this study is to determine the effect of using visual media (leaflets) in health promotion about immunization. This research is a pre-experimental study with One Group Pretest-Posttest Design. The data analysis technique used univariate and bivariate analysis. Univariate analysis was performed to see responden characterstic, while while bivariate data analysis was performed using the Wilcoxon test to see how visual media's effect to knowledge and behaviour of immunization. The result showed that health promotion using visual media, namely leaflets can significantly increase both the knowledge and behavior of mothers about immunization

The relationship of bivariate data ordinarily measured using correlation coefficient. The most commonly used correlation coefficient is the Pearson correlation coefficient. This coefficient is well-known as the best coefficient for interval or ratio bivariate data with a linear relationship. Even though this coefficient is good under the mentioned condition, it also becomes very sensitive to a small departure from linearity. Usually, this is because of the existence of an outlier. For that reason, this paper provides new robust correlation coefficients which combine the elements of nonparametric technique from the Hodges Lehmann estimator and the parametric technique based on the Pearson correlation coefficient. This paper also introduces different scale estimators such as median and median absolute deviation (MADn) and denoted by rHL(med) and rHL(MADn) respectively. The performance of the proposed correlation coefficients is measured by the coefficient values and these values are also being compared to the Pearson correlation coefficient and several existing robust correlation coefficients. The results show that the Pearson correlation coefficient (r) with no doubt is very good under perfect data condition, but with only 10% outliers, it not only give poor correlation value but turns the direction of the relationship to negative. While the rHL(med) and rHL(MADn) offer the highest coefficient values and these values are robust to the existence of outliers by up to 30%. With very good performance under all data conditions yet simple in the calculation, the rHL(med) and rHL(MADn) is considered a good alternative to the r when need to deal with outliers. Keywords: correlation coefficient; Hodges Lehmann; median; median absolute deviation (MADn)

Bivariate data consist of 2 random variables that are obtained from the same population. The relationship between 2 bivariate data can be measured by correlation coefficient. A correlation coefficient computed from the sample data is used to measure the strength and direction of a linear relationship between 2 variables. However, the classical correlation coefficient results are inadequate in the presence of outliers. Therefore, this study focuses on the performance of different correlation coefficient under contaminated bivariate data to determine the strength of their relationships. We compared the performance of 5 types of correlation, which are classical correlations such as Pearson correlation, Spearman correlation and Kendall’s Tau correlation with other robust correlations, such as median correlation and median absolute deviation correlation. Results show that when there is no contamination in data, all 5 correlation methods show a strong relationship between 2 random variables. However, under the condition of data contamination, median absolute deviation correlation denotes a strong relationship compared to other methods.

I re-examined the scaling of metabolic rate versus body mass in eight species of ant (static allometry) to illustrate one of the ways by which contemporary concepts of metabolic allometry have been negatively impacted by the widespread use of a standardized procedure for analyzing bivariate data. The procedure in question is the one promoted by Julian Huxley in his monograph on Problems of Relative Growth, and entails back-transforming the equation for a straight line fitted to logarithmic transformations of the original observations to form a two-parameter power function on the arithmetic scale. The scaling exponents for power equations fitted to data by Huxley’s protocol were used by the original authors to evaluate predictions from a theoretical model for the evolutionary optimization of body size in animals. However, my analyses—which were based on a different philosophy and protocol for modeling bivariate data—show that observations for each of the species can be described equally well by two or more different equations with different functional form. Metabolic rate is generally higher in large individuals than in small ones, but little more can be said about metabolic allometry in ants because a clear distinction cannot be made between alternative statistical models that require very different interpretations for biological importance. Conclusions from any investigation that relies exclusively on Huxley’s analytical protocol will be based on incomplete and potentially misleading evidence.

The proximity of businesses targeting the same market segment, meeting the same needs and operating in a similar way is generally believed to indicate more competition. However, this situation can be beneficial for the companies involved, and it may not necessarily generate an adverse environment. This study sought to analyse a group of restaurants that operate under similar conditions and that are located within the same area in order to identify the potential benefits and drawbacks of choosing this strategy to deal with market pressures. The research was based on a sample of 1,358 customers from 52 small restaurants. Diverse information-gathering techniques were combined such as observations, interviews and surveys. The data gathered was used to characterise different groups of variables’ behaviour based on descriptive statistics. In addition, bivariate statistics were utilised to test the hypotheses, while multivariate statistics were used to conduct correspondence analysis. The results reveal that, in the cases analysed, the parties involved benefit from the existing condition when a process of distribution of demand is present and advertising expenses are minimised.

Abstract. Studies of unconscious mental processes often compare a performance measure (e.g., some assessment of perception or memory) with a measure of awareness (e.g., a verbal report or forced-choice response) of the critical cue or contingency taken either concurrently or separately. The resulting patterns of bivariate data across participants lend themselves to several analytic approaches for inferring the existence of unconscious mental processes, but it is rare for researchers to consider the underlying generative processes that might cause these patterns. We show that bivariate data are generally insufficient to discriminate single-process models, with a unitary latent process determining both performance and awareness, from dual-process models, comprising distinct latent processes for performance and awareness. Future research attempting to isolate and investigate unconscious processes will need to employ richer types of data and analyses.

Stunting is a condition of failure to thrive in children under five due to chronic malnutrition. One cause of stunting is poor parenting patterns such as feeding in the first 2 years after birth. Exclusive breastfeeding is the best nutrition a baby receives in the first 6 months of life. The purpose of this study was to determine the relationship of exclusive breastfeeding with the decrease of stunting in children aged 6-23 months in Sosor Lontung Village, Siempat Nempu District, Dairi Regency. This study used a cross-sectional study design. The sample of this research was children aged 6-23 months as many as 39 people. Data collection was carried out by interview and measurement of children's length / height. Univariate and bivariate data analysis used Chi Square test with ƿ-value

This article proposes a space‐efficient approximation to empirical tail dependence coefficients of an indefinite bivariate stream of data. The approximation, which has stream‐length invari...

Resumen Existen diferentes métodos que permiten establecer a escalas regionales la susceptibilidad a la ocurrencia de movimientos en masa. Entre los métodos más utilizados se encuentran los métodos estadísticos bivariado y multivariado, los cuales exigen un inventario de procesos de remoción en masa. En el presente estudio se evalúa y zonifica la susceptibilidad por movimientos en masa en el norte de los Andes colombianos, región conocida como valle de Aburrá, por dos métodos estadísticos, uno de ellos bivariado, denominado Peso de la Evidencia, y recomendado por el Servicio Geológico Colombiano para estudios de amenaza en suelos rurales; y un segundo método estadístico tipo multivariado, denominado Regresión Logística, de amplio uso a nivel mundial. Para ambos casos, la construcción del modelo de susceptibilidad se realizó soportado en el histograma de frecuencias, correlación de Pearson, Análisis Discriminante y Análisis de Componentes Principales. Para evaluar el desempeño, la capacidad de predicción y los criterios de zonificación en alto, medio y bajo de cada uno de los métodos utilizados se utilizó el análisis ROC. Para la regresión logística se obtuvo un área bajo la curva del 76.8 % para el desempeño y 77.5 % para la capacidad de predicción, mientras que para el Peso de la Evidencia se obtuvo un 77.8 % en el desempeño y 77.5 % en la predicción, señalando resultados satisfactorios que permiten la incorporación de dichos resultados en los estudios básicos necesarios para la ordenación del territorio. Abstract Evaluating and zoning mass movement landslide is a fundamental tool for land planning. There are different methods that help to establish in a regional scale landslide hazard. The most common methods are bivariate statistics and multivariate statistic, which need a landslide historical inventory. This study takes a place in the North of the Andes in a region of Colombia called Aburrá Valley, for evaluating and zoning landslide susceptibility by two methods, one of them is bivariate statistics called Weights of Evidence which is recommended by the Geological Service of Colombia for rural area, and the second one is a multivariate statistic method, called logistic regression, which is widely used worldwide. Both methods are supported in frequency histogram, Pearson correlation, Discriminant Analysis, and Principal Component Analysis. The accuracy of the landslide susceptibility maps produced from the two models is classified in high, medium and low by ROC analysis. The AUC plot estimation results showed that the susceptibility map using Logistic regression has a training accuracy of 76.5% and a prediction capacity of 77.5 %. The Weights of evidence method has the highest training accuracy of 77.8 % and a prediction of 77.5 %. This result allows to include the methods in territorial planning studies.

Hormone assay results below the assay detection limit (DL) can introduce bias into quantitative analysis. Although complex maximum likelihood estimation methods exist, they are not widely used, whereas simple substitution methods are often used ad hoc to replace the undetectable (UD) results with numeric values to facilitate data analysis with the full data set. However, the bias of substitution methods for steroid measurements is not reported. Using a large data set (n = 2896) of serum testosterone (T), DHT, estradiol (E2) concentrations from healthy men, we created modified data sets with increasing proportions of UD samples (≤40%) to which we applied five different substitution methods (deleting UD samples as missing and substituting UD sample with DL, DL/√2, DL/2, or 0) to calculate univariate descriptive statistics (mean, SD) or bivariate correlations. For all three steroids and for univariate as well as bivariate statistics, bias increased progressively with increasing proportion of UD samples. Bias was worst when UD samples were deleted or substituted with 0 and least when UD samples were substituted with DL/√2, whereas the other methods (DL or DL/2) displayed intermediate bias. Similar findings were replicated in randomly drawn small subsets of 25, 50, and 100. Hence, we propose that in steroid hormone data with ≤40% UD samples, substituting UD with DL/√2 is a simple, versatile, and reasonably accurate method to minimize left censoring bias, allowing for data analysis with the full data set.

The complex relationship between water quality and river discharge has long been an active area of research. This research applies bivariate statistics to river nitrate concentration and discharge, and develops a procedure for selecting the best bivariate distribution for the chosen models. Nitrate concentration (NO3) data from five stations on the Lower Illinois River, USA, collected from 1972 to 2012 were used for demonstration of this procedure. To explore the statistical relationship between discharge and nitrate concentration, three copula statistical models were applied to determine optimal bivariate distributions. The generalized Pareto (GPA), generalized extreme value (GEV), and lognormal two- (LN2) and three-parameter (LN3) distributions were used as marginal distributions, and were combined with the Clayton, Frank, and Gumbel copula models. The probability plot correlation coefficient (PPCC) test and the S n statistic were used to select the most suitable copula models. As a result, the GPA distributions for streamflow and nitrate concentration in the Frank copula model were more accurate for representing the data from the two mainstem stations, Havana (D-31) and Valley City (D-32), and those from the Oakford station along the Sangamon River (E-25). However, the Clayton copula model using NL3 for representing streamflow and GPA for representing nitrate concentration was more accurate for stations along the Spoon (DJ-08) and La Moine Rivers (DG-01). This study enabled the development of a procedure for determining an optimal copula for application in the environmental sciences and also provided a case study for applying copula models using discharge and nutrient concentration as hydrologic and water quality variables, respectively.

We consider the problem of outlier detection method in 2×2 crossover design via Bayesian framework. We study the problem of outlier detection in bivariate data fitted using generalized linear model in Bayesian framework used by Nawama. We adapt their work into a 2×2 crossover design. In Bayesian framework, we assume that the random subject effect and the errors to be generated from normal distributions. However, the outlying subjects come from normal distribution with different variance. Due to the complexity of the resulting joint posterior distribution, we obtain the information on the posterior distribution from samples by using Markov Chain Monte Carlo sampling. We use two real data sets to illustrate the implementation of the method.

The Java software jBar consists of a graphical user interface that allows the user to customize and assemble an included script for R. The scripted R pipeline calculates means and standard errors/deviations for replicates of numerical bivariate data and generates presentations in the form of bar graphs. A two-sided Student's t test is carried out against a user-selected reference and p-values are calculated. The user can enter the data conveniently through the built-in spreadsheet and configure the R pipeline in the graphical user interface. The configured R script is written into a file and then executed. Bar graphs can be generated as static PNG, PDF, and SVG files or as interactive HTML widgets. © 2019 International Union of Biochemistry and Molecular Biology, 47(2): 207-210, 2019.

Copula functions have been extensively used in applied statistics, becoming a good alternative for modeling the dependence of multivariate data. Each copula function has a different dependence structure. An important issue in these applications is the choice of an appropriate copula function model for each one; thus common classical or Bayesian discrimination methods might not be appropriate for determining the best copula. Considering only the special case of bivariate data, we propose a procedure obtained from a recently introduced dependence measure for selecting an appropriate copula for the statistical data analyses.

Identifying, from time series analysis, reliable indicators of causal relationships is essential for many disciplines. Main challenges are distinguishing correlation from causality and discriminating between direct and indirect interactions. Over the years many methods for data-driven causal inference have been proposed; however, their success largely depends on the characteristics of the system under investigation. Often, their data requirements, computational cost or number of parameters limit their applicability. Here we propose a computationally efficient measure for causality testing, which we refer to as pseudo transfer entropy (pTE), that we derive from the standard definition of transfer entropy (TE) by using a Gaussian approximation. We demonstrate the power of the pTE measure on simulated and on real-world data. In all cases we find that pTE returns results that are very similar to those returned by Granger causality (GC). Importantly, for short time series, pTE combined with time-shifted (T-S) surrogates for significance testing strongly reduces the computational cost with respect to the widely used iterative amplitude adjusted Fourier transform (IAAFT) surrogate testing. For example, for time series of 100 data points, pTE and T-S reduce the computational time by $$82\%$$ 82 % with respect to GC and IAAFT. We also show that pTE is robust against observational noise. Therefore, we argue that the causal inference approach proposed here will be extremely valuable when causality networks need to be inferred from the analysis of a large number of short time series.

Landslide susceptibility assessment was conducted in Canada Hill, Sarawak, Malaysia through a combined bivariate statistics and expert consultation approach using geographical information system, which captures landslide-conditioning parameters specific to the study area; to ensure its usefulness in practice. Over the past four decades, many landslide parameters and increasingly sophisticated statistical methods have been used in landslide research. However, the findings have had very limited use in practice as the actual ground conditions are not well represented. The weakness is due to poor quality of data in landslide inventories and inadequate understanding of landslide-conditioning parameters. In this study, bivariate statistical method was used in conjunction with an iterative process of expert consultation. Thirteen original landslide-conditioning parameters were narrowed down to six, with the addition of a unique parameter, planar failure potential, which was selected based on expert input. The parameter captures planar failure landslides, which has the highest impact in the study area, causing loss of lives and property destruction. The inaugural landslide susceptibility map for the study area has five classes; very low, low, moderate, high and very high susceptibility. All major planar failures and most smaller circular failures fall within the very high susceptibility class, with a success rate of 75.8%. The approach used in this study has improved the quality of the landslide inventory and delineated key conditioning parameters. The resultant map captures local conditions, which is useful for landslide management.

When reconstructing sediment provenance, the challenge posed by multiple univariate (i.e., age-only) detrital geochronology data sets with similar one-dimensional distributions can be mitigated by incorporation of a second variable such as Hf isotopic data. However, there is no commonly applied method of sample intercomparison, much less forward or inverse modeling of these bivariate data sets. In this paper we explore application of non-negative matrix factorization (NMF) to bivariate data sets. Factorization of univariate mixed (a.k.a., sink or daughter) data sets has been demonstrated to successfully recover both the one-dimensional endmember (a.k.a., source or parent) distributions and their mixture weightings. We show that NMF can successfully recover both the two-dimensional distributions and mixing weights in synthetic data sets. Application of the method to 24 published Neoproterozoic–Triassic samples from western Laurentia yields six two-dimensional endmember distributions that are a close match to empirical sediment sources on the southern, eastern, and northern margin of Laurentia. The results are broadly consistent with previous interpretations and confirm that the method can characterize unknown sediment sources based on data from analyzed sink samples. Correlating between factorized endmembers and empirical sources indicates that the Transcontinental Arch was not a barrier to east–west sediment transport until the late Cambrian. Quantitative comparison also shows that the closest known match for a factorized endmember with highly evolved Permo-Triassic zircons is from northern South America and suggests northward transport of this detritus following assembly of Pangea. Recognizing these empirical sources and their distribution into strata that would later be incorporated into the North American Cordillera sets the stage for interpreting sediment provenance records in the Jurassic–Paleogene Cordilleran retroarc foreland basin. Supplementary material: The open-source software (DZnmf2D) and a user manual is available in public repositories: https://doi.org/10.5281/zenodo.4460336. All other supplemental files are available at https://doi.org/10.6084/m9.figshare.c.5280320 Thematic collection: This article is part of the Fold-and-thrust belts and associated basins collection available at: https://www.lyellcollection.org/cc/fold-and-thrust-belts

In this paper, we study the concomitants of dual generalized order statistics (and consequently generalized order statistics) when the parameters γ1,⋯,γn are assumed to be pairwise different from Huang–Kotz Farlie–Gumble–Morgenstern bivariate distribution. Some useful recurrence relations between single and product moments of concomitants are obtained. Moreover, Shannon’s entropy and the Fisher information number measures are derived. Finally, these measures are extensively studied for some well-known distributions such as exponential, Pareto and power distributions. The main motivation of the study of the concomitants of generalized order statistics (as an important practical kind to order the bivariate data) under this general framework is to enable researchers in different fields of statistics to use some of the important models contained in these generalized order statistics only under this general framework. These extended models are frequently used in the reliability theory, such as the progressive type-II censored order statistics.

Many clinical decisions are taken based on the results of continuous diagnostic tests. Usually, only the results of one single test is taken into consideration, the interpretation of which requires a reference range for the healthy population. However, the use of two different tests, can be necessary in the diagnosis of certain diseases. This obliges a bivariate reference region be available for their interpretation. It should also be remembered that reference regions may depend on patient variables (eg, age and sex) independent of the suspected disease. However, few proposals have been made regarding the statistical modeling of such reference regions, and those put forward have always assumed a Gaussian distribution, which can be rather restrictive. The present work describes a new statistical method that allows such reference regions to be estimated with no insistence on the results being normally distributed. The proposed method is based on a bivariate location-scale model that provides probabilistic regions covering a specific percentage of the bivariate data, dependent on certain covariates. The reference region is estimated nonparametrically and the nonlinear effects of continuous covariates via polynomial kernel smoothers in additive models. The bivariate model is estimated using a backfitting algorithm, and the optimal smoothing parameters of the kernel smoothers selected by cross-validation. The model performed satisfactorily in simulation studies under the assumption of non-Gaussian conditions. Finally, the proposed methodology was found to be useful in estimating a reference region for two continuous diagnostic tests for diabetes (fasting plasma glucose and glycated hemoglobin), taking into account the age of the patient Óscar Lado-Baleato is funded by a predoctoral grant (ED481A-2018) from the Galician Government (Plan I2C)-Xunta de Galicia. This research was also supported by grants from the Carlos III Health Institute, Spain (PI16/01404 and RD16/0017/0018), and by the project MTM2017-83513-R cofinanced by the Ministry of Economy and Competitiveness (SPAIN) and the European Regional Development Fund (FEDER). This work was also supported by grants from the Galician Government: RED INBIOEST (ED341D-R2016/032), Grupo de Referencia Competitiva (ED431C 2016-025), and Grupo de Potencial Crecimiento (IN607B 2018-1). Javier Roca-Pardiñas acknowledges financial support by the Grant MTM2017-89422-P (MINECO/AEI/FEDER, UE) SI

A novel, general two-sample hypothesis testing procedure is established for testing the equality of tail copulas associated with bivariate data. More precisely, using an ingenious transformation of a natural two-sample tail copula process, a test process is constructed, which is shown to converge in distribution to a standard Wiener process. Hence, from this test process a myriad of asymptotically distribution-free two-sample tests can be obtained. The good finite-sample behavior of our procedure is demonstrated through Monte Carlo simulations. Using the new testing procedure, no evidence of a difference in the respective tail copulas is found for pairs of negative daily log-returns of equity indices during and after the global financial crisis.

In this article we describe a new Hermite series based sequential estimator for the Spearman rank correlation coefficient and provide algorithms applicable in both the stationary and non-stationary settings. To treat the non-stationary setting, we introduce a novel, exponentially weighted estimator for the Spearman rank correlation, which allows the local nonparametric correlation of a bivariate data stream to be tracked. To the best of our knowledge this is the first algorithm to be proposed for estimating a time varying Spearman rank correlation that does not rely on a moving window approach. We explore the practical effectiveness of the Hermite series based estimators through real data and simulation studies demonstrating good practical performance. The simulation studies in particular reveal competitive performance compared to an existing algorithm. The potential applications of this work are manifold. The Hermite series based Spearman rank correlation estimator can be applied to fast and robust online calculation of correlation which may vary over time. Possible machine learning applications include, amongst others, fast feature selection and hierarchical clustering on massive data sets., Revised article incorporating comments by the reviewers, associate editor and editor of the Journal of Multivariate Analysis (accepted manuscript). Changes include a modified title and a significantly shortened article

This paper proposes a new class of covariance functions for bivariate random fields on spheres, having the same properties as the bivariate Matern model proposed in Euclidean spaces. The new class depends on the geodesic distance on a sphere; it allows for indexing differentiability (in the mean square sense) and fractal dimensions of the components of any bivariate Gaussian random field having such covariance structure. We find parameter conditions ensuring positive definiteness. We discuss other possible models and illustrate our findings through a simulation study, where we explore the performance of maximum likelihood estimation method for the parameters of the new covariance function. A data illustration then follows, through a bivariate data set of temperatures and precipitations, observed over a large portion of the Earth, provided by the National Oceanic and Atmospheric Administration Earth System Research Laboratory.

Multivariate datasets with a clustered structure are the natural framework for, e.g., multicentre clinical trials. We propose a number of methods aimed at detecting clusters with outlying correlation coefficients. While the methods can be used in a variety of settings, we focus mainly on their application to central statistical monitoring of clinical trials. In particular, we consider the issue of detecting centers (or other clusters of patients such as regions) with outlying correlation coefficients for bivariate data in a multicenter clinical trial. It appears that, in that context, the proposed methods perform well, as we show by using a simulation study and a number of real life datasets.

In this work, we investigate the asymptotic behavior of the extremes of a multivariate data by using the Reduced Ordering Principle (R-ordering). When, the sup-norm is used, we reveal the interrelation between the R-ordering principle and Marginal Ordering Principle (M-ordering). The asymptotic behavior of the maximum sup-norms corresponding to the bivariate data is completely determined. Finally, an application to real data illustrates and corroborates the theoretical results.

Episodes of frequent flooding continue to increase, often causing serious damage and tools to identify areas affected by such disasters have become indispensable in today's society. Using the latest techniques can make very accurate flood predictions. In this study, we introduce four effective methods to evaluate the flood susceptibility of Poyang County, in China, by integrating two independent models of frequency ratio and index of entropy with multilayer perceptron and classification and regression tree models. The flood locations of the study area were identified through the flood inventory process, and 12 flood conditioning factors were used in the training and validation processes. According to the results of the linear support vector machine, elevation, slope angle, and soil have the highest predictive ability. The experimental results of the four hybrid models demonstrate that between 20% and 50% of the study area has high and very high flood susceptibility. The multilayer perceptron-probability density hybrid model is the most effective among the six comparative methods.

Detailed resource or impact assessment studies often call for higher spatial resolution data products. Remote sensing data e.g., SAR (Synthetic Aperture Radar) provide high spatial resolution wind information but suffer from the satellite’s relatively poor revisit time. This paper focuses on the preliminary assessment of offshore wind speed derived from diverse data sources, characterized by different spatial and temporal resolution. A univariate statistical analysis and a match-up comparison between in-situ Cyprus meteorological stations wind speed measurements and Sentinel-1A and 1B VV-polarized SAR wind field estimates were conducted for a two-year period between 1st June, 2017-1st June, 2019. Results indicate that SAR data overestimate the in-situ measurements resulting in an average bias of 0.7 m/s, which was gradually increasing in parallel to the wind speed values. Errors also proved to vary spatially with Akrotiri demonstrating the highest average errors comparing to Pafos and Larnaca. Despite the discrepancies found, Sentinel-1 SAR Level-2 OCN can be considered as a reliable source for offshore wind field estimation. The initial assessment presented in this paper can be considered as the basis for a future in-depth analysis of Cyprus offshore wind resource assessment.

In this research, vegetation indices (VIs) were analyzed as indicators of the spatio-temporal variation of vegetation in a semi-arid region. For a better understanding of this dynamic, interactions between vegetation and climate should be studied more widely. To this end, the following methodology was proposed: (1) acquire the NDVI, EVI, SAVI, MSAVI, and NDMI by classification of vegetation and land cover categories in a monthly period from 2014 to 2018, (2) perform a geostatistical analysis of rainfall and temperature, and (3) assess the application of ordinary and uncertainty least squares linear regression models to experimental data from the response of vegetation indices to climatic variables through the BiDASys (bivariate data analysis system) program. The proposed methodology was tested in a semi-arid region of Zacatecas, Mexico. It was found that besides the high values in the indices that indicate good health, the climatic variables that have an impact on the study area should be considered given the close relationship with the vegetation. A better correlation of the NDMI and EVI with rainfall and temperature was found, and similarly, the relationship between VIs and climatic factors showed a general time lag effect. This methodology can be considered in management and conservation plans of natural ecosystems, in the context of climate change and sustainable development policies.

Damage assessment is a key element in structural health monitoring of various industrial applications to understand well and predict the response of the material. The big uncertainty in carbon fiber composite materials response is because of variability in the initiation and propagation of damage. Developing advanced tools to design with composite materials, methods for characterizing several damage modes during operation are required. While there is a significant amount of work on the analysis of acoustic emission (AE) from different composite materials and many loading cases, this research focuses on applying an unsupervised clustering method for separating AE data into several groups with distinct evolution. In this paper, we develop an adaptive sampling and unsupervised bivariate data clustering techniques to characterize the several damage initiations of a composite structure in different lay-ups. An adaptive sampling technique pre-processes the AE features and eliminates redundant AE data samples. The reduction of unnecessary AE data depends on the requirements of the proposed bivariate data clustering technique. The bivariate data clustering technique groups the AE data (dependent variable) with respect to the mechanical data (independent variable) to assess the damage of the composite structure. Tensile experiments on carbon fiber reinforced composite laminates (CFRP) in different orientations are carried out to collect mechanical and AE data and demonstrate the damage modes. Based on the mechanical stress-strain data, the results show the dominant damage regions in different lay-ups of specimens and the definition of the different states of damage. In addition, the states of the damage are observed using Scanning Electron Microscope (SEM) analysis. Based on the AE data, the results show that the strong linear correlation between AE and mechanical energy, and the classification of various modes of damage in all lay-ups of specimens forming clusters of AE energy with respect to the mechanical energy. Furthermore, the validation of the cluster-based characterization and improvement of the sensitivity of the damage modes classification are observed by the combined knowledge of AE and mechanical energy and time-frequency spectrum analysis.

Understanding correlation judgement is important to designing effective visualizations of bivariate data. Prior work on correlation perception has not considered how factors including prior beliefs and uncertainty representation impact such judgements. The present work focuses on the impact of uncertainty communication when judging bivariate visualizations. Specifically, we model how users update their beliefs about variable relationships after seeing a scatterplot with and without uncertainty representation. To model and evaluate the belief updating, we present three studies. Study 1 focuses on a proposed ''Line + Cone'' visual elicitation method for capturing users' beliefs in an accurate and intuitive fashion. The findings reveal that our proposed method of belief solicitation reduces complexity and accurately captures the users' uncertainty about a range of bivariate relationships. Study 2 leverages the ``Line + Cone'' elicitation method to measure belief updating on the relationship between different sets of variables when seeing correlation visualization with and without uncertainty representation. We compare changes in users beliefs to the predictions of Bayesian cognitive models which provide normative benchmarks for how users should update their prior beliefs about a relationship in light of observed data. The findings from Study 2 revealed that one of the visualization conditions with uncertainty communication led to users being slightly more confident about their judgement compared to visualization without uncertainty information. Study 3 builds on findings from Study 2 and explores differences in belief update when the bivariate visualization is congruent or incongruent with users' prior belief. Our results highlight the effects of incorporating uncertainty representation, and the potential of measuring belief updating on correlation judgement with Bayesian cognitive models., Comment: 9 pages, 8 figures, accepted at IEEE Information Visualization 2020

Robust prediction of extreme motions during wind farm support vessel (WFSV) operation is an important safety concern. In particular, it is important to study safety of operation in random sea conditions during WFSV docking against the wind tower, while workers are able to get on to the tower. Docking is performed by thrusting the vessel fender against the wind tower (the alternative docking maneuver by hinging is not studied here). In this paper, the finite element software AQWA has been used to analyse the vessel response due to hydrodynamic wave loads, acting on a specific maintenance ship under actual sea conditions. Excessive motions may occur during certain sea conditions, posing a risk to the crew transfer operation. This paper presents a novel method for estimating bivariate statistics, based on Monte Carlo simulations (or measurements if available). The bivariate average conditional exceedance rate (ACER2D) method is briefly outlined. This is an [Accepted Manuscript] of an article published by Taylor & Franci

Researchers often focus on bivariate normal correlation (r) to evaluate bivariate relationships. However, these techniques assume linearity and depend on parametric assumptions. We propose a new nonparametric statistical model that can be more intuitively understood than the conventional r: probability of bivariate superiority (PBS). Our development of Bp, the estimator of a PBS relationship, extends Dunlap’s (1994) common-language transformation of r (CLr) by providing a method to directly estimate PBS—the probability that when x is above (or below) the mean of all X, its paired y score will also be above (or below) the mean of all Y. Probability of superiority is an important form of bivariate relationship that until now could only be accurately estimated when data met the parametric assumptions for r. We specify the copula that forms the theoretical basis for PBS, provide an algorithm for estimating PBS from a sample, and describe the results of a Monte Carlo experiment that evaluated our algorithm across 448 data conditions. The PBS estimate, Bp, is robust to violations of parametric assumptions and offers a useful method for evaluating the significance of probability-of-superiority relationships in bivariate data. It is critical to note that Bp estimates a different form of bivariate relationship than does r. Our working examples show that a PBS effect can be significant in the absence of a significant correlation, and vice versa. In addition to utilizing the PBS model in future research, we suggest that this new statistical procedure be used to find theoretically important but previously overlooked effects from past studies.

A simple sorting approach for inducing any desired Pearson or Spearman correlation to independent bivariate data, whose marginals can be of any distributional type and nature is described and illus...

In this study we introduce a new method of adding two shape parameters to any baseline bivariate distribution function (df) to get a more flexible family of bivariate df's. Through the additional parameters we can fully control the type of the resulting family. This method is applied to yield a new two-parameter extension of the bivariate standard normal distribution, denoted by BSSN. The statistical properties of the BSSN family are studied. Moreover, via a mixture of the BSSN family and the standard bivariate logistic df, we get a more capable family, denoted by FBSSN. Theoretically, each of the marginals of the FBSSN contains all the possible types of df's with respect to the signs of skewness and excess kurtosis. In addition, each possesses very wide range of the indices of skewness and kurtosis. Finally, we compare the families BSSN and FBSSN with some important competitors (i.e., some generalized families of bivariate df's) via real data examples. AMS 2010 Subject Classification: 62-07; 62E10; 62F99.

This study focuses on a recently introduced type of indicator measuring disruptiveness in science. Disruptive research diverges from current lines of research by opening up new lines. In the current study, we included the initially proposed indicator of this new type (Funk & Owen-Smith, 2017; Wu, Wang, & Evans, 2019) and several variants with DI1: DI5, DI1n, DI5n, and DEP. Since indicators should measure what they propose to measure, we investigated the convergent validity of the indicators. We used a list of milestone papers, selected and published by editors of Physical Review Letters, and investigated whether this human (experts)-based list is related to values of the several disruption indicators variants and – if so – which variants show the highest correlation with expert judgements. We used bivariate statistics, multiple regression models, and (coarsened) exact matching (CEM) to investigate the convergent validity of the indicators. The results show that the indicators correlate differently with the milestone paper assignments by the editors. It is not the initially proposed disruption index that performed best (DI1), but the variant DI5 which has been introduced by Bornmann, Devarakonda, Tekles, and Chacko (2020a). In the CEM analysis of this study, the DEP variant – introduced by Bu, Waltman, and Huang (in press) – also showed favorable results.

A purely data-based index for detecting bivariate association is proposed for preliminary data exploration when seeking to model a dependent variable, associated with a possibly large number of independent variables. No particular form of association between the dependent and independent variables is assumed. The proposed bivariate association index is the value p , which is the probability that a scatter plot created by an X -randomization will generate a smaller mean nearest neighbour distance. The rationale is that randomizing an existing X-Y association will result in a scatter plot which will usually have a greater mean nearest neighbour distance. The process is then repeated for all other independent variables to give a specific p for each one. A subset of potentially informative independent variables is then obtained by noting all those with low p values, but just how small p should be is left to the user.

Rock glaciers are valuable diagnostic landforms indicating permafrost creeping during their genesis and activity. Based on the analysis of high quality air-orthophoto and field work, a first polygon-based inventory of rock glaciers from the Southern Carpathians has been elaborated. In total, 306 rock glaciers were included in the inventory comprising 79 debris and 227 talus rock glaciers. Most of these landforms were classified as relict (258), while only 48, covering 2.81 km 2 , were considered intact. The size of rock glaciers, considered as a proxy for past environmental conditions, and the relationships with the predictor variables (lithology, aspect, contributing area, geographic coordinates, elevation and slope range) were analysed using bivariate statistics, analysis of variance (ANOVA) and various post hoc tests. The statistical analysis revealed that the rock glaciers occurring in the highest mountain ranges in areas composed of granites and granodiorites are considerably larger than the others, because their duration of activity is greater. Strong dependences between rock glacier size and other topographic attributes (contributing area, aspect and slope range) were also confirmed. The rock glacier distribution in the Southern Carpathians is clearly controlled by topography, lithology and debris availability. The abundance of rock glaciers increases with altitude, but their size decreases slightly. In mountain units where granites and granodiorites predominate (Retezat and Parâng Mountains), the density of rock glaciers and the mean specific area covered by these spectacular landforms are considerably higher than in other areas. The higher continentality effects of the Southern Carpathians enabled the formation of rock glaciers at substantially lower elevations than in the Alps. The mean altitude of intact rock glaciers front, which could be used as a morphological indicator of discontinuous permafrost, is located at 2088 m.