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An approach to modelling volatile financial return series using stationary d-vine copula processes combined with Lebesgue-measure-preserving transformations known as v-transforms is proposed. By developing a method of stochastically inverting v-transforms, models are constructed that can describe both stochastic volatility in the magnitude of price movements and serial correlation in their directions. In combination with parametric marginal distributions it is shown that these models can rival and sometimes outperform well-known models in the extended GARCH family. 1

Noun phrase conjunction in Akan (Niger-Congo, Kwa) is performed by placing a connective between two noun phrases, but there is some variation in the forms used in the major dialects. In the Twi dialects the connective is ne, but Fante speakers may use nye or na depending on whether a comitative or a coordinative interpretation is intended. This paper focuses on the historical origins of the noun phrase connective n(y)e in Akan. It suggests that Akan patterns with other sub-saharan African languages such as Ewe, Ga, Yoruba and Hausa, which have noun phrase connectives originating from comitative verbs. This suggestion is based on the morpho-semantics of these connectives. In addition, the paper demonstrates that the origin of the connective n(y)e could be further traced to an equative copula in the language. This conclusion is based on syntactic and semantic evidence available in the language and strengthened by the cross-linguistic tendency for copula verbs to develop into noun phrase connectives in a number of unrelated languages.

The goal of the present research work is to develop a new family of aggregation operators (AOs) under the fractional orthotriple fuzzy (FOF) information and apply them to MCDM problems. At the start, the Archimedean coupla and co-coupla are extended to handle FOF information, and some operational law for fractional orthotriple fuzzy numbers (FOFNs) based on extended Archimedean copula (EAC) and extended Archimedean co-copula (EACC) is presented. The fractional orthotriple fuzzy Banzhaf Choquet-Copula aggregation operator and fractional orthotriple fuzzy Banzhaf Choquet-Copula geometric operators are defined based on the proposed operational laws of FOFNs. In addition, the modified maximum deviation approach and the Banzhaf function model are created to objectively determine the fuzzy measure (FM) of criteria sets. Finally, based on the defined AOs, the appropriate decision-making procedures are developed. The proposed approaches can effectively overcome the FMs of criteria sets that are subjectively assigned by decision makers, as well as some decision-making problems in which the weights of the criteria are incomplete (completely) unknown, and there is a correlation between all criteria set.

Economic and financial time series data can exhibit nonstationary and nonlinear patterns simultaneously. This paper studies copula-based time series models that capture both patterns. We introduce a procedure where nonstationarity is removed via a filtration, and then the nonlinear temporal dependence in the filtered data is captured via a flexible Markov copula. We propose two estimators of the copula dependence parameters: the parametric (two-step) copula estimator where the marginal distribution of the filtered series is estimated parametrically; and the semiparametric (two-step) copula estimator where the marginal distribution is estimated via a rescaled empirical distribution of the filtered series. We show that the limiting distribution of the parametric copula estimator depends on the nonstationary filtration and the parametric marginal distribution estimation, and may be non-normal. Surprisingly, the limiting distribution of the semiparametric copula estimator using the filtered data is shown to be the same as that without nonstationary filtration, which is normal and free of marginal distribution specification. The simple and robust properties of the semiparametric copula estimators extend to models with misspecified copulas, and facilitate statistical inferences, such as hypothesis testing and model selection tests, on semiparametric copula-based dynamic models in the presence of nonstationarity. Monte Carlo studies and real data applications are presented.

This work presents a derivative-free trust-region algorithm for probability maximization problems. We assume that the probability function is continuously differentiable with Lipschitz continuous gradient, but no derivatives are available. The algorithm explores the particular structure of the probability objective function through models based on copulae. Under reasonable assumptions, the global convergence of the algorithm is analyzed: we prove that all accumulation points of the sequence generated by the algorithm are stationary. The proposed approach is validated by encouraging numerical results on academic and industrial problems.

Recent advancements in generative networks have shown that it is possible to produce real-world-like data using deep neural networks. Some implicit probabilistic models that follow a stochastic procedure to directly generate data have been introduced to overcome the intractability of the posterior distribution. However, the ability to model data requires deep knowledge and understanding of its statistical dependence--which can be preserved and studied in appropriate latent spaces. In this article, we present a segmented generation process through linear and nonlinear manipulations in the same-dimensional latent space where data are projected to. Inspired by the known stochastic method to generate correlated data, we develop a segmented approach for the generation of dependent data, exploiting the concept of copula. The generation process is split into two frames: one embedding the covariance or copula information in the uniform probability space, and the other embedding the marginal distribution information in the sample domain. The proposed network structure, referred to as a segmented generative network (SGN), also provides an empirical method to sample directly from implicit copulas. To show its generality, we evaluate the presented approach in three application scenarios: a toy example, handwritten digits, and face image generation.

In this paper, we consider a new family of multivariate copulas described by a sequence of functions, named as AMO copula. The set of AMO copulas corresponds to a class of multivariate shock models with the Archimedean type of dependence. Sufficient conditions on the involved sequence of functions to obtain a multivariate copula are given and the probabilistic structure of the AMO copula is provided. We show that the family of AMO copulas is a generalization of Archimedean and Marshall-Olkin copulas family, and it includes some well-known copulas as specific cases. An alternative method for generating random vectors from AMO copulas via distortion functions is provided. In addition, a singular component along the main diagonal of the AMO copula is also verified. Finally, the tail behaviors of AMO copulas are discussed and some numerical illustrations are provided.

Considering the well-known shuffling operation in x- and in y-direction yields so-called double shuffles of bivariate copulas. We study continuity properties of the double shuffle operator S T induced by pairs T = ( T 1 × T 2 ) of measure preserving transformations on ( [ 0 , 1 ] , B ( [ 0 , 1 ] ) , λ ) on the family C of all bivariate copulas, analyze its interrelation with the star/Markov product, and show that for each left- and for each right-invertible copula A the set of all possible double shuffles of A is dense in C with respect to the uniform metric d ∞ . After deriving some general properties of the set Ω T of all S T -invariant copulas we focus on the situation where T 1 , T 2 are strongly mixing and show that in this case the product copula Π is an extreme point of Ω T . Moreover, motivated by a recent paper by Horanska and Sarkoci (Fuzzy Sets and Systems 378, 2018) we then study double shuffles induced by pairs of so-called Luroth maps and derive various additional properties of Ω T , including the surprising fact that Ω T contains uncountably many extreme points which (interpreted as doubly stochastic measures) are pairwise mutually singular with respect to each other and which allow for an explicit construction.

In this paper we find pointwise best-possible bounds on the set of copulas with a given value of the Spearman's footrule coefficient. We show that the lower bound is always a copula but, unlike the bounds on sets of copulas with a given value of other measures, such as Kendall's tau, Spearman's rho and Blonqvist's beta, the upper bound can be a copula or a proper quasi-copula. We characterised both of these cases.

This paper deals with the problem of characterizing all functions f : [ 0 , 1 ] → R + such that C f ( x , y ) = x y f ( ( 1 − x ) ( 1 − y ) ) , x , y ∈ [ 0 , 1 ] is a bivariate copula. We provide a complete characterization for the two cases: (i) when C f is, in addition, totally positive of order 2 (TP2) and (ii) when f is twice continuously differentiable. In general, the function f need only be twice differentiable Lebesgue almost everywhere as shown by investigating necessary conditions for C f to be a copula. The paper also contains numerous examples illustrating obtained results and connections to known facts from the literature. Moreover, several properties of such copulas are described.

In this article, we describe qregsel, a community-contributed command that implements a copula-based sample-selection correction for quantile regression recently proposed by Arellano and Bonhomme (2017, Econometrica 85: 1–28). The command allows the user to model selection in quantile regressions by using either a Gaussian or a one-dimensional Frank copula. We illustrate the use of qregsel with two examples. First, we apply the method to the fictional dataset used in the Stata Base Reference Manual for the heckman command. Second, we replicate part of the empirical application of the original article using data for the United Kingdom that cover the period 1978–2000 to compare wages of males and females at different quantiles.

Processability Theory (PT) is regarded as one of the prominent theory of second language acquisition (SLA) developed to illuminate the developmental sequences in SLA as well as some other linguistic phenomena (Pienemann, 1998a; 2011).Since 1990s, Processability has been at the center of attention in second language acquisition research. Within the framework of Processability theory and through analyzing the written performance of Iranian EFL learners, the present research focused on the acquisition of “Copula inversion” and “Negation” across five proficiency levels, from elementary to advanced and compared it with the stage-like development model of morpho-syntactic structures proposed by Pienemann (1998a, 2011). The study followed a descriptive method of research and the data was collected from 350 participants in five different proficiency levels from elementary, pre-intermediate, intermediate, upper-intermediate and advanced. The participants were asked to provide samples of their written performance on different tasks such as introduction task, habitual action task, story retelling task, audio-video-retelling task, picture description task, composition, communication task. The data in this research was analyzed both qualitatively, in order to identify and classify the type and order of the morpho-syntactic structures; and quantitatively, by calculating means. The results of Kruskal-Wallis test revealed that “Negation” emerged at the elementary level of the language learners’ performance and “copula inversion” emerged at the intermediate level. Just the same, the competence of the learner grows stronger in concern with these variables through the higher proficiency levels. These findings imply that PT is valid for Iranian EFL learners, as well.

The DEA is a nonparametric method of assessing the efficiency of decision-making units using mathematical programming. The classic DEA model assumes that input and output variables are deterministic. However, there are many applications where the variables are of a stochastic nature. Based on the consideration of input and output levels as random variables, the Stochastic Data Envelopment Analysis (SDEA) was developed. Statistical distributions therefore play a major role in this regard. By considering the dependency between input and output variables, and also their simultaneous dependencies in this study, we have introduced three copula-SCCR models. We used three copulas of Gaussian, Clayton, and Gumbel to estimate the dependence between the random variables with normal distribution. We evaluated the proposed models using real data from 20 bank branches. The results showed that considering stochastic dependency between the inputs or outputs causes different results. A comparison between the Copula-SCCR models and the SCCR models revealed that the efficiency of the DMUs using the Copula-SCCR models differed from the SCCR model by a significant margin of at least 20%.

Multivariate flood frequency analysis has been widely used in the design and risk assessment of hydraulic structures. However, analytical solutions are often obtained based on an idealized linear reservoir model in which a linear routing process is assumed, and consequently, the flood risk is likely to be over- or underestimated. The present study proposes a nonlinear reservoir model in which the relationships of reservoir water level with reservoir volume and discharge are assumed to be nonlinear in order to more accurately describe the routing process as it takes into consideration the interactions between hydrological loading and different discharge structures. The structure return period is calculated based on the copula function and compared with that based on the linear reservoir model and the bivariate return period based on the Kendall distribution function. The results show that the structure return period based on the linear model leads to an underestimation of the flood risk under the conditions of high reservoir water level. For the same reservoir, linear and nonlinear reservoir models give quite different reservoir volume-water level and discharge-water level curves; therefore, they differ substantially in the sensitivity to flood events with different combinations of flood peak and volume. We also analyze the effects of the parameters involved in the reservoir volume-water level and discharge-water level relationships on the maximum water level at different return periods in order to better understand the applicability and effectiveness of the proposed method for different hydraulic projects. HIGHLIGHTS The structure return period is calculated based on the nonlinear reservoir model.; Nonlinear relationships of water level with volume and discharge are assumed.; Interactions between hydrological loading and different structures are analyzed.; Effects of different storage and discharge capacity parameters are discussed.

This article discusses the aspect of modeling weather conditions in marine environment for implementation in the offshore wind farm domain. It is clear that harsh sea weather conditions influence many characteristics of any offshore installation. The accessibility to the infrastructure, maintenance procedures, failure ratios of components, energy provision levels, or utilization of vessels—are the examples of weather-related issues connected to the offshore wind industry. Regarding the growing popularity of digital twin methodology, authors present a novel view to generate weather data with copula-based method. The results obtained are compared to selected historical data and implemented into the maintenance model. The selected indicators of maintenance service are used for usability assessment of proposed copula-based method.

Seismic fragility assessment widely uses a probabilistic measure for assessing the seismic performance of structural components or systems. This article proposes a copula-based seismic fragility (CBSF) method to derive the system-level damage probabilities of reinforced concrete bridges and to consider the correlation among seismic demands of components. First, the marginal distribution functions of the random variables are calibrated, and three Archimedean copula models are considered. Subsequently, the relevant parameters of the copula models are estimated using the semi-parametric maximum likelihood method. Next, the damage probabilities of a bridge system are calculated based on the joint distribution model with the most suitable copula model and the calibrated marginal distribution functions. Finally, the CBSF method is used to estimate the damage probability of a simply supported box girder bridge. The performance of the CBSF method is validated by a comparison of fragility curves obtained using the CBSF method and the probabilistic seismic demand analysis (PSDA) method. The comparative results demonstrate that the fragility curves obtained by the CBSF method are better than those obtained using the PSDA method. The proposed CBSF model can serve as a tool for assessing the seismic performance of structures and estimating the economic loss of existing bridge systems.

Bivariate or multivariate survival data arise when a sample consists of clusters of two or more subjects which are correlated. This paper considers clustered bivariate survival data which is possibly censored. Two approaches are commonly used in modelling such type of correlated data: random effect models and marginal models. A random effect model includes a frailty model and assumes that subjects are independent within a cluster conditionally on a common non-negative random variable, the so-called frailty. In contrast, the marginal approach models the marginal distribution directly and then imposes a dependency structure through copula functions. In this manuscript, Bernstein copulas are used to account for the correlation in modelling bivariate survival data. A two-stage parametric estimation method is developed to estimate in the first stage the parameters in the marginal models and in the second stage the coefficients of the Bernstein polynomials in the association. Hereby we use a penalty parameter to make the fit desirably smooth. In this aspect linear constraints are introduced to ensure uniform univariate margins and we use quadratic programming to fit the model. We perform a Simulation study and illustrate the method on a real data set.

Multivariate modeling of dependence and its impact on risk assessment remains a major concern for financial institutions. Thus, the copula model, in particular Archimedean hierarchical copulas (HAC) appears as a promising alternative, capable to precisely capture the structure of dependence between financial variables. This study aims to widen the sphere of practical applicability of the HAC model combined with the ARMA-APARCH volatility forecast model and the extreme values theory (EVT). A sequential process of modeling of the VaR of a portfolio based on the ARMA-APARCH-EVT-HAC model is discussed. The empirical analysis conducted with data from international stock market indices clearly illustrates the performance and accuracy of modeling based on HACs.

Copula model is a method that can be implemented in various study fields, including analyzing wildfires. The copula distribution function gives a simple way to define joint distribution between two or more random variables. This study aims to review the application of copula in the analysis of wildfires using a Systematic Literature Review (SLR) and provide insight into research opportunities related to the application in Indonesia. The results show there are very few articles using the copula model in the analysis of wildfires. However, the increasing number of article citations each year shows the importance of such article research and has contributed to wildfire analysis development. In that article, 50% of studies applied the copula model to direct wildfire analysis (using fire data) in Canada, Portugal, and the US. Meanwhile, the other 50% use the copula model for indirect wildfire analysis (not using fire data) in Canada and the European region. The outcome of the presented review will provide the latest research positions and future research opportunities on the application of copula in the analysis of wildfires in Indonesia. Keywords: copula; wildfire; systematic literature review. Abstrak Model copula merupakan metode yang dapat diimplementasikan pada berbagai bidang penelitian, salah satunya pada analisis kebakaran hutan. Fungsi sebaran copula memberikan cara yang mudah untuk mendefinisikan sebaran peluang bersama antara dua peubah acak atau lebih. Tujuan penelitian ini mengulas penerapan model copula tersebut pada analisis kebakaran hutan dalam studi literatur menggunakan Systematic Literature Review (SLR) serta memberikan peluang riset ke depan terkait implementasinya pada analisis kebakaran hutan di Indonesia. Hasil penelitian menunjukkan bahwa model copula pada analisis kebakaran hutan masih sangat sedikit. Namun, peningkatan jumlah sitasi artikel tiap tahun menunjukkan pentingnya penelitian tersebut dan memiliki kontribusi pada perkembangan analisis kebakaran hutan. Pada artikel tersebut, sebanyak 50% penelitian menerapkan model copula pada analisis kebakaran secara langsung (menggunakan data kebakaran) di Kanada, Portugal, dan Amerika. Sementara, sebanyak 50% lainnya menerapkan model copula pada analisis kebakaran secara tak langsung (tidak menggunakan data kebakaran), yaitu di Kanada dan kawasan Eropa. Hasil tinjauan memberikan posisi riset terkini serta usulan riset ke depan mengenai penerapan model copula untuk analisis kebakaran hutan dan lahan di Indonesia . Kata kunci: copula ; kebakaran hutan; studi literatur sistematik .

In this article, we answer positively an open question posed in [G. Mayor, J. Suner, and J. Torrens, “Copula-like operations on finite settings,” IEEE Trans. Fuzzy Syst. , vol. 13, no. 4, pp. 468–477, Aug. 2005] concerning the extensions of discrete copulas to shuffles of Min. Moreover, we also use the extension of discrete copulas to sparse copulas, associated with discrete copulas, of idempotent copulas, in particular, the copula $M$ , in order to answer the open question in an alternative way.

Arabic syntax has yet to be studied in detail from a corpus-based perspective. The Arabic copula kāna (‘be’), functions also as an auxiliary, creating periphrastic tense–aspect constructions; but the literature on these functions is far from exhaustive. To analyse kāna within the one-million word Corpus of Contemporary Arabic, part-of-speech tagging (using novel, targeted enhancements to a previously described program which improves the accessibility for linguistic analysis of the output of Habash et al.’s [2012] mada disambiguator for the Buckwalter Arabic morphological analyser) is applied to disambiguate copula and auxiliary at a high rate of accuracy. Concordances of both are extracted, and 10 percent samples (499 instances of copula kāna and 387 of auxiliary kāna) are analysed manually to identify surface-level grammatical patterns and meanings. This raw analysis is then systematised according to the more general patterns’ main parameters of variation; special descriptions are developed for specific, apparently fixed-form expressions (including two phraseologies which afford expression of verbal and adjectival modality). Overall, we uncover substantial new detail, not mentioned in existing grammars (e.g., the quantitative predominance of the past imperfect construction over other uses of auxiliary kāna). There exists notable potential for these corpus-based findings to inform and enhance not only grammatical descriptions but also pedagogy of Arabic as a first or second/foreign language.

The Copula approach for continuous variables is highly developed, while discrete ones are underdeveloped due to computational difficulties and sometimes algorithm failure to convergent. Therefore, providing an alternative method for discrete variables becomes an essential issue. In this paper, a simple method is proposed to answer the problem by applying the Continuous Extension Technique (CET). This is carried out by adding random independent perturbations in the form of either Uniform distribution U(0,1) or (U(0,1)−1), and the discrete variables are treated as continuous. Subsequently, a Copula model for resulted variables is estimated based on the Copula theory for continuous variables. This method is called a Copula continuous extension technique. Our analytic and simulation approaches show that both random perturbation forms produce the same Kendall’s Tau measure and the selected Copula bivariate model. As illustrations, the proposed method is applied to the seismicity data obtained from the annual frequencies of earthquakes that occurred in the Sumatra megathrust of Indonesia, from January 1971 to December 2018, with magnitudes ( Mw ) of at least 4.6. Based on the selected Copula models, our simulations confirm the evidence of dependence seismic activity in each of the two adjacent large earthquake sources. These results provide new information regarding the seismicity behavior in the Sumatra megathrust.

The paper analyzes the morphosyntactic status of a copula no as part of complex verbal predicates of Guinean Pular. A locative copula no, combined with various forms of lexical verb, adds up to three verbal constructions. Morphological and semantic non-compositionality of no in such constructions questions its morphosyntactic status as a free word and suggests that it might be an affix or a clitic. Pular data has been subjected to a series of tests using a set of phonological, morphological, and semantic criteria. The results of the phonological tests show that no in complex verbal predicates cannot be a free word, whereas the morphological tests deny it the status of an affix. It is, therefore, concluded that this copula is a clitic, which is confirmed by the language data complying with general morphological and phonological criteria.

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.

Correlations among survival endpoints are important for exploring surrogate endpoints of the true endpoint. With a valid surrogate endpoint tightly correlated with the true endpoint, the efficacy of a new drug/treatment can be measurable on it. However, the existing methods for measuring correlation between two endpoints impose an invalid assumption: correlation structure is constant across different treatment arms. In this article, we reconsider the definition of Kendall's concordance measure (tau) in the context of individual patient data meta-analyses of randomized controlled trials. According to our new definition of Kendall's tau, its value depends on the treatment arms. We then suggest extending the existing copula (and frailty) models so that their Kendall's tau can vary across treatment arms. Our newly proposed model, a joint frailty-conditional copula model, is the implementation of the new definition of Kendall's tau in meta-analyses. In order to facilitate our approach, we develop an original R function condCox.reg(.) and make it available in the R package joint.Cox ( https://CRAN.R-project.org/package=joint.Cox ). We apply the proposed method to a gastric cancer dataset (3288 patients in 14 randomized trials from the GASTRIC group). This data analysis concludes that Kendall's tau has different values between the surgical treatment arm and the adjuvant chemotherapy arm ( p-value

We characterize the cumulative distribution functions and copulas of two-dimensional self-similar Ito processes, with randomly correlated Wiener margins, as solutions of certain elliptic partial differential equations.

For multivariate distributions in the domain of attraction of a max-stable distribution, the tail copula and the stable tail dependence function are equivalent ways to capture the dependence in the upper tail. The empirical versions of these functions are rank-based estimators whose inflated estimation errors are known to converge weakly to a Gaussian process that is similar in structure to the weak limit of the empirical copula process. We extend this multivariate result to continuous functional data by establishing the asymptotic normality of the estimators of the tail copula, uniformly over all finite subsets of at most $D$ points ($D$ fixed). An application for testing tail copula stationarity is presented. The main tool for deriving the result is the uniform asymptotic normality of all the $D$-variate tail empirical processes. The proof of the main result is non-standard., Comment: 33 pages, 1 figure

Agriculture is one of the main pillars of economic growth in Indonesia. Failure in this sector can result in faltering economic stability of the country. Thus, to minimize these failures, mapping of areas with particular commodity potential is needed. One of the main factors affecting the growth of crops is rainfall. Therefore, this paper aims to model the potential distribution of commodity growth based on rainfall precipitation using dynamic copula. The modeling results are then used as a basis for grouping the potential of food crop commodities in Indonesia. The determination of the group was carried out using the k-means clustering method. We expect that the result of the modeling can provide an overview for farmers or the government to make policies related to the optimization of Indonesia's agricultural sector. This result will enable the government to offer facilities that can minimize agricultural losses, such as superior seeds that are resistant to weather changes and the provision of training for enhancing farming skills. In addition, it is also suggested to diversify farm areas to reduce the failures due to dependence on a single agricultural product.

The Markov chain is well studied and widely applied in many areas. For some Markov chains, it is infeasible to obtain the explicit expressions of their corresponding finite-dimensional distributions and sometimes it is time-consuming for computation. In this paper, we propose an approximation method for Markov chains by applying the copula theory. For this purpose, we first discuss the checkerboard copula-based Markov chain, which is the Markov chain generated by the family of checkerboard copulas. This Markov chain has some appealing properties, such as self-similarity in copulas and having explicit forms of finite-dimensional distributions. Then we prove that each Markov chain can be approximated by a sequence of checkerboard copula-based Markov chains, and the error bounds of the approximate distributions are provided. Employing the checkerboard copula-based approximation method, we propose a sufficient condition for the geometric β-mixing of copula-based Markov chains. This condition allows copulas of Markov chains to be asymmetric. Finally, by applying the approximation method, analytical recurrence formulas are also derived for computing approximate distributions of both the first passage time and the occupation time of a Markov chain, and numerical results are listed to show the approximation errors.

Copula is one of the widely used techniques to describe the dependency structure between components of a system. Among all existing copulas, the family of Archimedean copulas is the popular one due to its wide range of capturing the dependency structures. In this paper, we consider the systems that are formed by dependent and identically distributed components, where the dependency structures are described by Archimedean copulas. We study some stochastic comparisons results for series, parallel, and general $r$-out-of-$n$ systems. Furthermore, we investigate whether a system of used components performs better than a used system with respect to different stochastic orders. Furthermore, some aging properties of these systems have been studied. Finally, some numerical examples are given to illustrate the proposed results.

This study deals with the stochastic comparison of extreme order statistics from random samples with FGM copula or FGM survival copula. For general marginal distributions, several sufficient condit...

The objective of this work is to estimate the patterns of dependence between the yields of the stock prices of the main banks of the United States (US) and Mexico. We estimate the patterns of absolute dependence and tail dependence through copulas of the Archimedean family and the use of rolling windows of 245 days. The data employed come from the daily share prices at closing from January 2, 2015, to December 31, 2020, for seven banks. Our results show that: i) there are patterns of high dependence among the main banks in the US, ii) there are patterns of very low dependence among the main banks in the US and Mexico, and iii) there are patterns of low dependence among the main banks in Mexico. These results have several implications, among them that the high-dependency patterns obtained among major US banks limit the joint selection of these US bank equity assets in an investment portfolio. Although this paper focuses on a small sample of banks, they represent an important portion of the banking sector in both countries. Given the limited literature on this subject in Mexico, our paper contributes to expanding this literature with a novel approach.

Knowledge plays a vital role in multi-attribute group decision-making (MAGDM), where experts from different-fields present their knowledge to support decision-making by employing multi-granularity linguistic model. The main goals of current work are targeted to present a novel MAGDM approach by integrating the extended Archimedean Copulas (EACs), group-individual best-worst method (GIBWM) and multi-attributive border approximation area comparison (MABAC) approach to fuse multi-source knowledge with multi-granularity intuitionistic 2-tuple linguistic information (I2TLI) with unknown weight information of attributes and experts. To begin with, for the sake of modeling the relationships between attributes (experts), the Copula-based aggregation operators with I2TLI are recommended together with some of its variations discussed; In addition, taking the merits of GIBWM methods, an algorithm of weight information of expert and attributes is designed; Thirdly, considering the decision maker’s behaviour preference and psychology, a modified MABAC method is proposed by modified prospect matrix. Simultaneously, an algorithm for MAGDM based on I2TLI with different granularity is designed by integrating GIBWM and modified MABAC approach. Last of all, an example is furnished to manifest the significance of the proposed method along with related discussions, the advantages of this method are analyzed by comparing with the extant decision-making approaches.

A new four-parameter lifetime model is introduced and studied. The new model derives its flexibility and wide applicability from the well-known exponentiated Weibull model. Many bivariate and the multivariate type versions are derived using the Morgenstern family and Clayton copula. The new density can exhibit many important shapes with different skewness and kurtosis which can be unimodal and bimodal. The new hazard rate can be decreasing, J-shape, U-shape, constant, increasing, upside down and increasing-constant hazard rates. Various of its structural mathematical properties are derived. Graphical simulations are used in assessing the performance of the estimation method. We proved empirically the importance and flexibility of the new model in modeling various types of data such as failure times, remission times, survival times and strengths data.

For a typical insurance portfolio, the claims process for a short period, typically one year, is characterized by observing frequency of claims together with the associated claims severities. The collective risk model describes this portfolio as a random sum of the aggregation of the claim amounts. In the classical framework, for simplicity, the claim frequency and claim severities are assumed to be mutually independent. However, there is a growing interest in relaxing this independence assumption which is more realistic and useful for the practical insurance ratemaking. While the common thread has been capturing the dependence between frequency and aggregate severity within a single period, the work of Oh et al. (2021) provides an interesting extension to the addition of capturing dependence among individual severities. In this paper, we extend these works within a framework where we have a portfolio of microlevel frequencies and severities for multiple years. This allows us to develop a factor copula model framework that captures various types of dependence between claim frequencies and claim severities over multiple years. It is therefore a clear extension of earlier works on one-year dependent frequency-severity models and on random effects model for capturing serial dependence of claims. We focus on the results using a family of elliptical copulas to model the dependence. The paper further describes how to calibrate the proposed model using illustrative claims data arising from a Singapore insurance company. The estimated results provide strong evidences of all forms of dependencies captured by our model.

The present study investigates the relationship between discourse integration skills and Spanish copula choice in monolingual Chilean Spanish-speaking children. Previous research has focused on determining the age at which children associateestarto a transitory property andserto an inherent property (Holtheuer, Carolina. 2012. Spanish-speaking children do not always overuse estar.Revista Signos45(78). 3–19, Holtheuer, Carolina & Johanna Rendle-Short. 2013. Ser and estar: Corrective input to children’s errors of the Spanish copula verbs.First Language33(2). 155–167, Schmitt, Cristina & Karen Miller. 2007. Making discourse dependent decisions: The case of the copulas ser and estar in Spanish.Lingua117(11). 1907–1929, Sera, Maria. 1992. To be or to be: Use and acquisition of the Spanish copulas.Journal of Memory and Language31. 408–427, Requena, Pablo, Astrid Román-Hernández & Karen Miller. 2015. Children’s knowledge of the Spanish copulas ser and estar with novel adjectives.Language Acquisition: A Journal of Developmental Linguistics22. 193–207), showing that by 2 years of age children know the categorial distribution of the two copulas, but that at 5 years of age only some children, but not all children, have knowledge of the transitory/inherent distinction that often arises when the same adjective occurs with one or the other copula. The present study seeks to extend the latter research by further investigating the factors that might influence why only some children associateestarto transitory properties at 5 years of age, a question that will not only shed light onwhenthe subtle meaning differences of the copulas are acquired, but alsohowthey are acquired. Maienborn, Claudia (2005. A discourse-based account of Spanish ser/estar.Linguistics43(1). 155–180) notes thatestaris discourse-linked, whileseris not. Specifically, the use ofestarwith an adjectival predicate to compare changes to a person across different stages of their life relies on one’s ability to integrate the larger discourse (i.e., these various stages) into their statement. In the present study, to determine whether Spanish-speaking children’s production of the copulaestarwith adjectival predicates was associated with their discourse integration abilities, children were presented with both a Copula Elicitation Task and a Discourse Production Task. Analyses revealed an association between children’s discourse integration skills and their use ofestarwith adjectives to express transitory properties, a finding that indicates that children’s acquisition ofestaris mastered late – at least in part because of their late development of discourse integration skills more generally. Most studies on the acquisition ofestarwith adjectival complements have focused primarily on comprehension. Experimental studies on children’sproductionofestarare rare. As such, this experimental study is one of the few that examines children’s use ofestarin production and the first, as far as we know, that provides empirical support for the link between discourse integration skills in children and their use ofestarwith adjectival predicates.

In this paper, we seek to examine the relationship and dynamic dependence structure between the Australian dollar (AUD), euro (EUR), and the British pound (GBP), expressed in American dollars (USD) using a multivariate fractional cointegration model. Our empirical analysis reveals several important findings. First, the main advantage of this approach is to detect the long-term relationship as well as the short-term dynamics and to represent the interdependence between the variables. We further estimate a multivariate GARCH type model that enables us to examine the dynamic conditional correlations (short-run links) among the considered variables under the effects of long-run interactions and volatility persistence. We determine that the volatility transmission was time-varying and that influence from the crisis. Moreover, the joint distribution is explored using the Gumbel copulas in order to describe the nonlinear structure of dependence between the variables. The empirical results provide evidence of fractional cointegration between the exchanges rates and show long-run causal links between the variables and we find significant bidirectional causal links. In particular, we show a positive dynamic correlation and the dependence structure is represented by the optimal copula coefficient used for measuring the risk spillovers between the exchange rates.