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The present study aims to enrich the specialized literature by proposing and calculating a new flash-flood propagation susceptibility index (FFPSI). Thus, firstly the Flash-Flood Potential Index (F...

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.

This article is intended to assess the flood-induced landslide susceptibility in the Indian state of Assam. This study area has high frequency and severity of landslides that are triggered by heavy...

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 “

The present work tried to develop multiparametric statistical and machine learning models of wetland water richness at two phases in the pre-dam period and at one phase in the post-dam period. Eigh...

A new, exact and closed-form expression is presented for the Beaulieu-Xie (BX) phase-envelope joint distribution. In addition, bivariate statistics are also determined for the BX distribution: the bivariate probability density function (PDF) of the envelope, the bivariate PDF of the instantaneous signal to noise ratio (SNR) and the generalized joint moment of the envelope, with and without correlation between the in-phase and quadrature components. Theoretical curves are plotted for different parameter values that characterize the fading.

The primary objective is to propose and verify an ensemble approach based on fuzzy system and bivariate statistics for landslide susceptibility assessment (LSA) at Azarshahr Chay Basin (Iran). In this regard, various integrations of fuzzy membership value (FMV), frequency ratio (FR), and information value (IV) with index of entropy (IOE) were investigated. Aerial photograph interpretations and substantial field checking were used to identify the landslide locations. Out of 75 identified landslides, 52 (≈70%) locations were utilized for the training of the models, whereas the remaining 23 (≈30%) cases were employed for the validation of the models. Fourteen landslide conditioning factors including altitude, slope aspect, slope degree, lithology, distance to fault, curvature, land use, distance to river, topographic position index (TPI), topographic wetness index (TWI), stream power index (SPI), normalized difference vegetation index (NDVI), distance to road, and rainfall were prepared and utilized during the analysis. The $$\mathrm{FMV}\_\mathrm{IOE}$$ , $$\mathrm{FR}\_\mathrm{IOE}$$ , and $$\mathrm{IV}\_\mathrm{IOE}$$ models were designed utilizing the dataset for training. Finally, to validate as well as to compare the model’s predictive abilities, the statistical measures of receiver operating characteristic (ROC), including sensitivity, accuracy, and specificity, were employed. The accuracy of 92.7, 92.5, and 91.8% of the models such as $$\mathrm{FMV}\_\mathrm{IOE}$$ , $$\mathrm{FR}\_\mathrm{IOE}$$ , and $$\mathrm{IV}\_\mathrm{IOE}$$ ensembles, respectively, was by the area under the receiver operating characteristic (AUROC) values developed from the ROC curve. For the validation dataset, the $$\mathrm{FMV}\_\mathrm{IOE}$$ model had the maximum sensitivity, accuracy, and specificity values of 95.7, 91.3, and 87.0%, respectively. Thus, the ensemble of FMV_IOE was introduced as a promising and premier approach that could be used for LSA in the study area. Also, IOE results indicated that altitude, lithology, and slope degree were main drivers of landslide occurrence. The results of the present research can be employed as a platform for appropriate basined management practices in order to plan the highly susceptible zones to landslide and hence minimize the expected losses.

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.

In this paper, we introduce uncertainty to continuous scatterplots and continuous parallel coordinates. We derive respective models, validate them with sampling-based brute-force schemes, and present acceleration strategies for their computation. At the same time, we show that our approach lends itself as well for introducing uncertainty into the definition of fibers in bivariate data. Finally, we demonstrate the properties and the utility of our approach using specifically designed synthetic cases and simulated data.

I used linear and nonlinear regression to re-examine the allometric relationship between length of the cephalic horn and width of the pronotum (a measure of body size) for males of 28 species of rhinoceros beetle (Coleoptera, Scarabaeidae, Dynastinae). An earlier investigation reported that variation in relative size of the horn conforms in most of the 28 species to a pattern of discontinuous, loglinear allometry, which implies, in turn, that two different power equations are needed to describe the full range in untransformed data. My analyses indicate, however, that allometric variation is continuous in all 28 species and that pattern in each of the original bivariate distributions is well described by a single mathematical function. Allometric variation on the original, arithmetic scale is linear for some species; either linear or slightly sigmoidal for other species; and decidedly sigmoidal in still other species. So-called major and minor morphs merely represent the extremes in absolute and relative size for the horn on animals drawn from the same, continuous distribution. The different findings reported in the earlier investigation resulted from insidious problems introduced by logarithmic transformation of the original bivariate data coupled with an overly complex statistical protocol for classifying individual males as either “major” or “minor.” Attempts at classification lead inevitably to oversimplification and misrepresentation of the pattern of allometric variation. Focus needs to return to describing and interpreting pattern in untransformed observations because the relationship between the original variables is the relationship of interest.

Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival times (e.g., matched pairs experiment, twin or family data), the shared frailty models were suggested. These models are based on the assumption that frailty acts multiplicatively to hazard rate. In this paper, we assume that frailty acts additively to hazard rate. We introduce the positive stable shared frailty models with three different baseline distributions namely, the generalized log-logistic and the generalized Weibull distributions. We introduce the Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in these models. We apply these models to a real-life bivariate survival data set of McGilchrist and Aisbett (Biometrics 47:461–466, 1991) related to the kidney infection data and a better model is suggested for the data.

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

In this work, we utilise a recently developed method of constructing a bivariate distributional model to generate a new bivariate distribution with Weibull and Burr type XII distributions as its marginals. Some general characteristics of this newly generated distribution together with some characterization results are further derived. The maximum likelihood method of estimation is applied for the estimation of the parameters of the constructed distribution. The closeness of the maximum likelihood estimators with the true values of the parameters have been illustrated through a simulation study. We have identified the generated model as a suitable model for a real life bivariate data set reported in the literature. We have also used another bivariate data set on geoelectrical variables X and Y in which X represents the aquifer thickness and Y represents the coefficient of anisotropy to illustrate the results described in this paper for bivariate distributional modelling.

Accurate estimation of extreme wind and wave conditions is critical for ocean engineering activities and applications. Various renewable energy offshore structures, particularly floating wind turbines are designed to sustain extreme wind and wave induced loads. Statistics of wind speeds and wave heights is the key input for structural safety and reliability study. Consequently, development of novel robust methods, able to predict extreme wind-wave conditions is essential. This paper discusses criteria for selecting design point by applying recently developed method for estimating extreme wave statistics, based on the hourly wave height and wind speed maxima at the location of interest. Wave and wind data, analyzed in this paper, was obtained from the hindcast model applied to the SEM-REV offshore sea location, near the coast of France, during years 2001–2010. The ECMWF (European Centre for Medium range Weather Forecasting) framework along with the atmospheric model SKIRON were employed to generate accurate hindcast wind-wave hourly data at the location of interest. Note that the SEM-REV site was built within the framework of the CPER (Contrat de Projet Etat-Region) 2007–2013 for the Pays de la Loire region, therefore it is important to note that 2001–2010 data studied in this paper was obtained by hindcast into the time period before SEM-REV began operations. Structural design values are often based on univariate statistical analysis, while actually multivariate statistics is more appropriate for modelling the whole structure. The bivariate analysis of extremes is often poorly understood and generally not adequately considered in most practical measurements/situations, therefore it is important to utilize recently developed bivariate average conditional exceedance rate (ACER2D) method. This paper studies extreme wind speeds and wave heights, that are simultaneously obtained at the same location. Due to less than full correlation between wind speed and wave height, application of the multivariate, or bivariate in the simplest case, extreme value theory is of practical importance. This paper focuses on application of the bivariate ACER2D method for prediction of bivariate extreme value statistics. Finally, this paper suggests how the design point should be chosed based on bivariate analysis. The latter is of particular engineering importance as it presents first application of bivariate wind-wave statistics to a raw SEM-REV site data.

In this work, we investigate the asymptotic behaviour of the intermediate and central order statistics of a bivariate data by using the Reduced Ordering Principle (R-ordering). When, the sup-norm i...

Methods to compare two samples of interval-valued data are discussed. In the interval-valued data, observations have the form of intervals and are often read as two-dimensional vector of lower and upper bounds. We consider four methods, two of which are the applications of existing methods for bivariate data, and the other two are based on the marginalization (univariate distributional representation) of the interval-valued data. We conduct a comprehensive numerical study and analysis of real data to understand the performance of four methods.

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)

This study examined domestic and international long-distance travel patterns of Reykjavik residents. We applied a mixed-methods approach with data triangulation to three datasets, two quantitative and one qualitative. Quantitative analyses included bivariate statistics, spatial statistics, and regression, and qualitative analysis included an explanatory interpretation of semi-structured interviews. The study found a higher number of international trips made by people residing close to the main city centre, particularly among younger adults. Following previous literature, we studied five potential groups of explanations of these patterns: 1) socioeconomic and demographic characteristics, 2) monetary rebound effects, 3) compensation or escape hypothesis, 4) lifestyles and other socio-psychological characteristics, and 5) dispersion of social networks. We found that all these aspects explain the travel activity to some extent, but inconsistently across the different datasets except for the well-known impact of socioeconomic and demographic characteristics. However, above all else, a cosmopolitan attitude in travel and language skill level were found to be the most influential predictors of international travel activity, and access to a summer house was an important predictor of domestic travel activity. Broad social networks were also found to play an important role. Despite geographical trends, the study did not find any strong causal relationship between urban form and long-distance travel that would influence the aggregate patterns. Thus, the results do not challenge the urban planning policies of densification on the premise of causing an unintended increase in emissions from long-distance travel.

Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival times, the s...

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.

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