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Journal articles on the topic 'Copulas'
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1
Chiravate, Boonjeera. "Aspectual Properties and Polarity-Sensitivity of Copulas pen1 and khʉʉ1 in Thai." MANUSYA 15, no. 1 (2012): 1–18. http://dx.doi.org/10.1163/26659077-01501001.
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‘Pen1’ and ‘khʉʉ1’ in Thai have traditionally been regarded as copular verbs comparable to ‘be’ in English. Appearing in a copulative sentence, the two Thai copula verbs, however, differ in polarity-sensitivity. The present study demonstrates that the difference in polarity-sensitivity of the two Thai copulas cannot be accounted for within the theory of polarity-sensitive items previously proposed. Investigating the aspectual properties of the two Thai copulas in comparison with those of English copula, this study suggests that an explanation for the difference in polarity-sensitivity of the two Thai copulas might involve their aspectual properties. Contributing to the study of aspect and polarity-sensitivity, the present study reveals differences between Thai and English copulas and provides additional support for the idea that the macro-category of so-called copular verbs is too vague to describe cross-linguistic variation.
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Welch, Nicholas, and Marie-Louise Bouvier White. "Copular clauses in Dene languages: Argument structure and interpretation." Canadian Journal of Linguistics/Revue canadienne de linguistique 66, no. 2 (June 2021): 223–54. http://dx.doi.org/10.1017/cnj.2021.12.
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AbstractA widely accepted assumption in both the syntactic and semantic literature is that copulas lack semantic content. A consequent question is how to explain the existence in certain languages of two copular verbs that give rise to different interpretations. Such is the case in numerous languages of the Dene family (formerly known as Athapaskan). We explain this situation with the hypothesis that the copulas realize an underlying three-copula system differing in argument structure. Differences between the interpretations of copular clauses in these languages originate in the compositional semantics of these structures, not in any lexical semantic differences.This hypothesis successfully predicts the distributional differences between the surface forms of the Dene copulas, such as their compatibility with adjuncts of time and intentionality, interactions with accusative case, and semantic lifetime effects.
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Mikulskas, Rolandas. "Descriptive problems in defining the category of copulas: syntactic and semantic distribution of the ingressive copulas VIRSTI and TAPTI." Lietuvių kalba, no. 12 (December 15, 2018): 1–63. http://dx.doi.org/10.15388/lk.2018.22519.
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Cognitive Grammar (Langacker 1991) allows for a unified account of copular constructions. In this framework, all types of copular constructions can be seen as the different instantiations of a single archetype of statements of identity between two entities (Mikulskas 2017). Radical Construction Grammar, the framework adopted in this article, also allows for a unified account of copular verbs, as it views both so-called ‘semi-copulas’ and typical copulas as members of a single category of copulas as long as each of them fills the same slot between the thematic argument and the predicative complement in a copular construction. According to Radical Construction Grammar, an independent word class ‘copula’ does not exist. “Instead, verbs in a particular language can be labelled ‘copular’ if they have the appropriate semantics and morphosyntax to fit in the so-called ‘copular slot’ of a copular construction” (Petré 2012: 30). From this theoretical perspective, the term ‘copula’ applies only derivatively. Thus, syntactically, copular verbs have a linking function. Additionally, some of them express various aspectual meanings and can be seen as aspectual variants of the typical copula “be”. For instance, the Lithuanian verbs tapti ‘become’, virsti ‘turn into’, darytis/pasidaryti ‘become’ (lit. ‘make oneself’) and, formerly, stotis/pastoti ‘become’ (lit. ‘stand up’), mainly in the Simple Past and Future tenses, when used in copular constructions, express ingressive aspect of the change event. These verbs, used in different constructions, such as existential, locomotional etc., retain their original meaning. Importantly, even when they are used in copular constructions, while being first of all linking verbs and aspectual markers, they can still have different syntactic and semantic properties. The latter are the outcome of their primary meanings inherited from their source constructions (‘backward pull’; Traugott 2008). That said, it is nevertheless clear that each of these verbs is in a different stage on its way to grammaticalization and each accommodated to copular function in a varying degree. So, a descriptivist encounters a practical problem: which of the above-mentioned verbal lexemes qualify as ‘real’ copulas and which do not? Are such verbs as augti ‘grow’ or eiti ‘go’, which can perform copular function in certain restricted contexts, on a par with more typical copulas such as tapti or virsti? Some Lithuanian researchers even doubt if the verb lexeme virsti can be labelled ‘copular’. To provide for this descriptive need a definition of the category of copulas is elaborated in the first two chapters of the article. Complementing the constructional requirement of filling the slot between the thematic argument and the predicative complement, two additional criteria are suggested. First, the postcopular nominal, as the result of reanalysis of the source construction in the course of grammaticalization, must become coreferential with the subject nominal. This is a necessary but not sufficient condition, as it does not differentiate between primary and secondary predicatives. Secondly, the types of complement of the verb must be unpredictable from its semantics or, in other words, the copular verb must be desemanticized to a sufficient degree to be capable of selecting its complements from a wide array of semantic and syntactic types (that is, NP, ADJ, PP). So the question whether to include a concrete verb lexeme into the class of copulas is mainly reduced investigating the semantics of its complements (or the productivity of its complementation). In the second two chapters of the article a contrastive study of the syntactic and semantic properties of the copular verbs virsti vs. tapti is presented in order to prove that the corresponding copular constructions featuring these verbs are different instantiations of the more abstract ingressive-aspect-expressing construction. A quantitative analysis of data in the Corpus of Modern Lithuanian reveals various relevant points in the parallel development and interaction of these verbs and in their coexistence in present-day Lithuanian: how they divide between them the job of expressing ingressive aspect in the profiled change events while at the same time competing with each other in some contexts. Additionally, some relevant facts of the usage of the copulas under discussion were checked in the Old Lithuanian Corpus and in the Dictionary of the Lithuanian Language. The analysis allows us to draw some important conclusions concerning the coexsistence of the two verbs under discussion and their categorial status in modern Lithuanian. First of all, the verb virsti can reasonably be seen as an aspectual variety of the copula būti ‘be’, on a par with the more grammaticalized copula tapti. The verb virsti, when used in copular constructions, is sufficiently desemanticized: one may claim that a sufficient number of copular constructions featuring the verb virsti have nearly lost their touch with their inherent semantics. More specifically, half of the analysed cases of copular constructions with this verb have already abandoned their tendency – inherited from the locomotional source construction (designating the overturning of a vertical object ) – to denote negatively evaluated change events. Though the verb virsti was originally used mainly in the inclusive type of copular constructions, it is now, on the analogy of copular constructions featuring the verb tapti, increasingly used in the ascriptive type as well: in more than 4% of the analysed instances the copula virsti selects adjectival predicative complements. Sporadically, the copula virsti is attested even in the specificational type of copular constructions (in this type of sentences the usage of the copula tapti is unrestricted). Also in modern Lithuanian the copula virsti has borrowed from the copular constructions featuring tapti the morphosyntactic coding of its complements by the instrumental instead of the original coding with PP. A thorough study of the semantic distribution of the copulas virsti and tapti in the Corpus of Modern Lithuanian shows that they have more or less divided between them the semantic space of aspectual expression according to the meanings they have inherited from their source constructions, and to their resulting aspectual potential. The constructions containing the copula virsti profile, in most cases, a radical transformation of a subject referent proceeding in an uncontrolled and incremental way. Such transformations include changes of physical elements, changes in a person’s mood and character, or spell-induced changes in fairy tales. Aspectually, such copular constructions have the profile of an accomplishment. Conversely, the constructions featuring the copula tapti presuppose a subject referent in control of the profiled change event. The result of the change is usually a new social status, a new profession or office held by the subject referent. In some cases the change profiled is only a projection of some relevant features of the subject referent into the cognitive domain of some speech community: the subject referent of the sentence, because of its social behaviour or personal features, is declared by the speaker to be a model or a guide for other people. The aspectual profile of such constructions is typically that of an achievement as in most cases they designate an instantaneous ingression of the subject referent into its new status. Nevertheless, the quantitative analysis of the corpus data shows that in about 13% of the copular constructions analysed the preterite verbal forms virto and tapo can be used interchangeably. This fact, considered together with the empirically attested facts of mutual interaction of the corresponding copular constructions, allows us to treat the constructions featuring these copular forms as two different instantiations of a single copular construction expressing the ingressive aspect of the profiled change event.
4
Fuchs, Sebastian, and Yann McCord. "On the lower bound of Spearman’s footrule." Dependence Modeling 7, no. 1 (May 11, 2019): 126–32. http://dx.doi.org/10.1515/demo-2019-0005.
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AbstractÚbeda-Flores showed that the range of multivariate Spearman’s footrule for copulas of dimension d ≥ 2 is contained in the interval [−1/d, 1], that the upper bound is attained exclusively by the upper Fréchet-Hoeffding bound, and that the lower bound is sharp in the case where d = 2. The present paper provides characterizations of the copulas attaining the lower bound of multivariate Spearman’s footrule in terms of the copula measure but also via the copula’s diagonal section.
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Petré,, Peter. "General productivity: How become waxed and wax became a copula." Cognitive Linguistics 23, no. 1 (February 2012): 27–65. http://dx.doi.org/10.1515/cog-2012-0002.
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AbstractThis article provides an analysis—within the framework of Radical Construction Grammar—of how become developed into a copula ‘become’ out of an original sense ‘arrive’, and wax, originally ‘grow’, also came to be used as a copula ‘become’. Importantly, it explains why these verbs successfully became fully productive copulas in a very short period of time. It is argued that this happened after a pre-copular stage had reached a cognitive threshold value. The occurrence of this threshold is related to the fact that the copular constructions featuring become and wax were not the end result of a single diachronic lineage of constructions (i.e. one construction developed out of another one, one at a time). Instead, the copularization of these verbs was the result of an interaction between lineages of constructions, belonging to two groups: (i) constructions involving become or wax, which gradually changed and interacted with each other; (ii) constructions involving already existing copulas, notably weorđan ‘become’, which provided a generally productive analog upon which the newly emerging copulas could graft. Generally, the article calls attention to the importance of multiple source constructions and thresholds in understanding grammaticalization processes and productivity.
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Alanazi, Fadhah Amer. "Truncating Regular Vine Copula Based on Mutual Information: An Efficient Parsimonious Model for High-Dimensional Data." Mathematical Problems in Engineering 2021 (October 20, 2021): 1–11. http://dx.doi.org/10.1155/2021/4347957.
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Based on (different) bivariate copulas as simple building blocks to model complex multivariate dependency patterns, vine copulas provide flexible multivariate models. They, however, lose their flexibility with dimensions. Attempts have been existing to reduce the model complexity by searching for a subclass of truncation vine copulas, of which only a limited number of vine trees are estimated. However, they are either time-consuming or model-dependent or require additional computational efforts. Inspired by the relationship between copula’s parameters (and the corresponding Kendall’s tau) and the mutual information on the one side and the mutual information and copula entropy on another side, this study proposed a novel truncation vine copula model using only mutual information values among variables. This newly proposed truncation method is evaluated in simulation studies and a real application of financial returns dataset. The simulated and real studies show that the model is sufficiently good to find the most appropriate truncation level with a good fit of a given data.
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Xie, Jiehua, Jun Fang, Jingping Yang, and Lan Bu. "MULTIVARIATE COMPOSITE COPULAS." ASTIN Bulletin 52, no. 1 (November 3, 2021): 145–84. http://dx.doi.org/10.1017/asb.2021.30.
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AbstractIn this paper, we present a method for generating a copula by composing two arbitrary n-dimensional copulas via a vector of bivariate functions, where the resulting copula is named as the multivariate composite copula. A necessary and sufficient condition on the vector guaranteeing the composite function to be a copula is given, and a general approach to construct the vector satisfying this necessary and sufficient condition via bivariate copulas is provided. The multivariate composite copula proposes a new framework for the construction of flexible multivariate copula from existing ones, and it also includes some known classes of copulas. It is shown that the multivariate composite copula has a clear probability structure, and it satisfies the characteristic of uniform convergence as well as the reproduction property for its component copulas. Some properties of multivariate composite copulas are discussed. Finally, numerical illustrations and an empirical example on financial data are provided to show the advantages of the multivariate composite copula, especially in capturing the tail dependence.
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Aldhufairi, Fadal Abdullah-A., Ranadeera G. M. Samanthi, and Jungsywan H. Sepanski. "New Families of Bivariate Copulas via Unit Lomax Distortion." Risks 8, no. 4 (October 14, 2020): 106. http://dx.doi.org/10.3390/risks8040106.
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This article studies a new family of bivariate copulas constructed using the unit-Lomax distortion derived from a transformation of the non-negative Lomax random variable into a variable whose support is the unit interval. Existing copulas play the role of the base copulas that are distorted into new families of copulas with additional parameters, allowing more flexibility and better fit to data. We present general forms for the new bivariate copula function and its conditional and density distributions. The properties of the new family of the unit-Lomax induced copulas, including the tail behaviors, limiting cases in parameters, Kendall’s tau, and concordance order, are investigated for cases when the base copulas are Archimedean, such as the Clayton, Gumbel, and Frank copulas. An empirical application of the proposed copula model is presented. The unit-Lomax distorted copula models outperform the base copulas.
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Edwards, H. H., P. Mikusiński, and M. D. Taylor. "Measures of concordance determined byD4-invariant copulas." International Journal of Mathematics and Mathematical Sciences 2004, no. 70 (2004): 3867–75. http://dx.doi.org/10.1155/s016117120440355x.
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A continuous random vector(X,Y)uniquely determines a copulaC:[0,1]2→[0,1]such that when the distribution functions ofXandYare properly composed intoC, the joint distribution function of(X,Y)results. A copula is said to beD4-invariant if its mass distribution is invariant with respect to the symmetries of the unit square. AD4-invariant copula leads naturally to a family of measures of concordance having a particular form, and all copulas generating this family areD4-invariant. The construction examined here includes Spearman’s rho and Gini’s measure of association as special cases.
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Aminullah, Salsabila Zahra, Mila Novita, and Ida Fithriani. "Vine Copula Model: Application to Chemical Elements in Water Samples." Proceedings of The International Conference on Data Science and Official Statistics 2023, no. 1 (December 29, 2023): 572–85. http://dx.doi.org/10.34123/icdsos.v2023i1.346.
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Copula can link the bivariate distribution function with marginal distribution functions without requiring specific information about the interdependence among random variables. There are several types of copulas, such as elliptical copulas, Archimedean copulas, and extreme value copulas. However, in multivariate modeling, each type of copula has limitations in modeling complex dependence structures in terms of symmetry and tail dependence properties. The class of vine copulas overcomes these limitations by constructing multivariate models using bivariate copulas in a tree-like structure. The bivariate copulas used in this study include the Clayton, Gumbel, Frank, Gaussian, and Student's t copula families. This study discusses the construction of vine copula models, parameter estimation, and their applications. The construction of vine copulas is done through the decomposition of conditional probability density functions and substituting bivariate copula density functions into the decomposition results. The data used in the study is the logarithm of the concentration of chemical elements in water samples in Colorado. The parameter estimation method used is pseudo-maximum likelihood with sequential estimation. Model selection is then performed using the Akaike information criterion (AIC) to determine the most suitable model. The results indicate that Caesium and Titanium have a dependency relationship with Scandium. Moreover, Scandium and Titanium exhibit the strongest dependence compared to other variable pairs.
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Mikulskas, Rolandas. "Aspectual variation in Lithuanian copular constructions." Lietuvių kalba, no. 9 (December 18, 2015): 1–49. http://dx.doi.org/10.15388/lk.2015.22627.
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In this article an attempt is made to pinpoint all possibilities of expressing aspectual meanings in Lithuanian copular constructions. The author departs from the tradition of distinguishing only perfective vs. imperfective aspect in Lithuanian. Instead, in testing various possibilities of expressing aspect in the constructions under discussion, the relevant meanings are chosen from a wider range of aspectual grams established in recent typological work on aspect.Until now the aspect of copular constructions had remained an understudied and underdescribed topic not only in Lithuanian. This is because the main concern of linguists has been with general problems of predication (or identification) in equative structures. Researchers (mainly of the formal persuasion) have based their accounts on copular sentences where the copula “be”, more specifically its present tense form, is taken to be the default case. Of course such ‘default’ copular constructions deliver an unproblematic aspectual meaning, that of imperfective state. Empirically, however, present tense (or zero) copulas are the default instance only in the case of identificational equatives, for identity statements typically assert general truths that are ‘timeless’ or ‘omnitemporal’. As this research has shown, the remaining types of copular constructions have a much wider potential for choosing the desired aspectual meaning. First of all, the functional−structural properties of these constructions and the contexts in which they are used provide much more space for aspect−tense variation in their copular verbs than in the default cases of identificational equatives. Secondly, the aspectual properties of the copular construction can be changed externally by introducing, at clausal level, specialized adverbials or periphrastic aspectual constructions, such as jau ‘already’, du kartus ‘twice’, buvo be-tampąs, bet… ‘he was about to become, but…’ etc.; in this case the aspectual interpretation of the copula is coerced in line with the overall aspectual profile of the construction. Thirdly, the range of aspectual meanings in the copular constructions becomes even wider if we take into account other copulas than “be”, viz. those of dynamic or locative origin. The typological research of recent decades in this field (Stassen 1997; Pustet 2003) has shown that cross-linguistically it is not unusual for copulas to be grammaticalized from different lexical sources. One may reasonably suppose that one of the motives for including new lexemes in the class of copulas was the need of expressing relevant aspectual meanings in the predication of identity, i.e. in various types of copular constructions. So languages tend to have, in addition to their main copula, a small number of verbs that can qualify as copulas and that mainly serve the needs of aspectual expression in their constructions. In Lithuanian these copular verbs are tapti, pasidaryti / darytis ‘become’, virsti ‘turn into’, likti ‘remain’. Depending on their tense and syntactic environment, ‘dynamic’ copulas can express ingressive, progressive or habitual aspect. The copula likti denotes continuation of the profiled situation, as does the prefixed form tebe-būti (tebe-(nebe-) being the usual marker of (phasal / aspectual) continuative meaning in Lithuanian).In the article due attention is also paid to the aspectual properties of the different types of copular constructions. In his earlier works the author has provided a new classification based on the idea of type instantiation, developed by Ronald Langacker (1991). In the second section of this paper these types are briefly passed in review, but the classification is updated and enriched with new discussion. The main idea behind the new classification is that all types of copular constructions are treated as instantiations of one archetype, that of the identity relation. What distinguishes these constructional types is the syntactic class of their predicative complements (adjective vs. noun) and additionally, in the case of predicative nominals, their referential properties. Before turning, in the fourth section, to a discussion of concrete aspectual meanings as expressed in different types of copular constructions, the author first makes a brief excursion, in the third section, to the typology of strategies for encoding predicatives as defined in Leon Stassen’s comprehensive typological study on intransitive predication (1997). This seemed necessary as one may suspect that variation in this domain of morphosyntactic encoding is to a great extent motivated by the need of expressing additional aspectual meanings in the constructions under discussion.
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Zachariah, Swaroop Georgy, Mohd Arshad, and Ashok Kumar Pathak. "A new family of copulas based on probability generating functions." Mathematica Slovaca 74, no. 4 (August 1, 2024): 1039–60. http://dx.doi.org/10.1515/ms-2024-0076.
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Abstract We propose a method to obtain a new class of copulas using a probability generating function (PGF) of positive-integer valued random variable. Some existing copulas in the literature are sub-families of the proposed copulas. Various dependence measures and invariant property of the tail dependence coefficient under PGF transformation are also discussed. We propose an algorithm for generating random numbers from the PGF copula. The bivariate concavity properties, such as Schur concavity and quasi-concavity, associated with the PGF copula are studied. Two new generalized FGM copulas are introduced using PGFs of geometric and discrete Mittag-Leffler distributions. The proposed two copulas improved the Spearman’s rho of FGM copula by (−0.3333, 0.4751) and (−0.3333, 0.9573). Finally, we analyse a real dataset to illustrate the practical application of the proposed copulas.
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Welch, Nicholas. "Differential grammaticalization of copulas in Tsúùt’ínà and Tłı̨chǫ Yatıì." Diachronica 36, no. 2 (July 22, 2019): 262–93. http://dx.doi.org/10.1075/dia.15031.wel.
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Abstract The languages of the Dene (aka Athapaskan) family in North America almost universally employ two copular verbs. In several languages of this family, copular forms are also employed as verbal auxiliaries: forms of one copula mark clausal focus while forms of the other mark TAM (tense/aspect/mode) categories. With reference to two Dene languages in particular, Tłı̨chǫ Yatıì and Tsúùt’ínà, I explain this difference by positing distinct grammaticalization paths and motivations for each copula: both focus and TAM markers originate in a uniclausal reanalysis of biclausal constructions, the former from constructions where the matrix clause asserts the truth of the embedded clause, and the latter from those where the matrix clause supplies extra TAM information to the embedded clause. Both grammaticalizations involve an upward reanalysis of copulas as functional heads.
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Pap, Endre, and Marta Takács. "Two-Dimensional Copulas as Important Binary Aggregation Operators." Journal of Advanced Computational Intelligence and Intelligent Informatics 10, no. 4 (July 20, 2006): 522–26. http://dx.doi.org/10.20965/jaciii.2006.p0522.
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We introduce 2-copulas (copulas, shortly) and recent related research results. We present invariant copulas and their application in the theory of aggregation operators. Copulas are transformed by increasing bijections at the unit interval and discuss copula attractors. We also present results on the approximation of associative copulas by strict and nilpotent triangular norms.
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Fazeres-Ferradosa, Tiago, Francisco Taveira-Pinto, Erik Vanem, Maria Teresa Reis, and Luciana das Neves. "Asymmetric copula–based distribution models for met-ocean data in offshore wind engineering applications." Wind Engineering 42, no. 4 (July 11, 2018): 304–34. http://dx.doi.org/10.1177/0309524x18777323.
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Joint statistical models for long-term wave climate are a key aspect of offshore wind engineering design. However, to find a joint model for sea-state characteristics is often difficult due to the complex nature of the wave climate and the physical constraints of sea-states phenomena. The available records of wave heights and periods are often very asymmetric in their nature. This article presents a copula-based approach to obtain the joint cumulative distribution function of the significant wave heights and the up-crossing mean period. This study is based on 124-month hindcast data concerning Horns Rev 3 offshore wind farm. The extra-parametrization technique of symmetric copulas is implemented to account for the asymmetry present in the data. The analysis of the total sea, the wind-sea and primary swell components is performed separately. The results show that the extra-parametrization technique with pairwise copulas consistently provided a better goodness-of-fit when compared to symmetric copulas. Moreover, it is demonstrated that the separation of the total sea into its components does not always improve the extra-parametrized copula’s performance. Furthermore, this article also discusses copulas application to offshore wind engineering.
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El maazouz, Mohamed, and Ahmed Sani. "New asymmetric perturbations of FGM bivariate copulas and concordance preserving problems." Moroccan Journal of Pure and Applied Analysis 9, no. 1 (January 1, 2023): 111–26. http://dx.doi.org/10.2478/mjpaa-2023-0008.
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Abstract New copulas, based on perturbation theory, are introduced to clarify a symmetrization procedure for asymmetric copulas. We give also some properties of the symmetrized copula mainly conservation of concordance. Finally, we examine some copulas with a prescribed symmetrized part. The start point of the treatment is the independence copula and the last one will be an arbitrary member of Farlie-Gumbel-Morgenstein family. By the way, we study topologically, the set of all symmetric copulas and give some of its classical and new properties.
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Silvagni, Federico. "When estar is not there: A cross-linguistic analysis of individual/stage-level copular sentences in Romance." Open Linguistics 8, no. 1 (January 1, 2022): 108–32. http://dx.doi.org/10.1515/opli-2022-0186.
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Abstract This article studies how Romance languages encode the individual-level (IL)/stage-level (SL) aspectual distinction in the domain of non-verbal predication. To this end, attributive copular clauses are considered, and those languages that mark the IL/SL paradigm by means of two different copulas (ser and estar ‘to be’, such as Spanish, Catalan, and Portuguese) are compared with mono-copular languages (such as French, Italian, and Romanian). On the basis of recent developments in the study of the IL/SL contrast and Spanish copulas, I propose that SL-ness is encoded in non-verbal SL-predicates as an uninterpretable instance of a [Stage] feature and that SL-copular sentences are derived by virtue of an agreement operation between the predicate and an Asp head that carries an interpretable instance of [Stage], which is realised as estar in languages such as Spanish, Portuguese, and Catalan. The conclusion is that the inventory of aspectual elements is the same across Romance languages, which differ one from another with respect to the presence of an SL-copula (namely, estar).
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Hofert, Marius, and Johanna F. Ziegel. "Matrix-Tilted Archimedean Copulas." Risks 9, no. 4 (April 6, 2021): 68. http://dx.doi.org/10.3390/risks9040068.
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The new class of matrix-tilted Archimedean copulas is introduced. It combines properties of Archimedean and elliptical copulas by introducing a tilting matrix in the stochastic representation of Archimedean copulas, similar to the Cholesky factor for elliptical copulas. Basic properties of this copula construction are discussed and a further extension outlined.
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Kamaruzaman, Izzat Fakhruddin, Wan Zawiah Wan Zin, and Noratiqah Mohd Ariff. "A generalized bivariate copula for flood analysis in Peninsular Malaysia." Malaysian Journal of Fundamental and Applied Sciences 15, no. 1 (February 4, 2019): 38–49. http://dx.doi.org/10.11113/mjfas.v15n2019.1275.
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This study generalized the best copula to characterize the joint probability distribution between rainfall severity and duration in Peninsular Malaysia using two dimensional copulas. Specifically, to construct copulas, Inference Function for Margins (IFM) and Canonical Maximum Likelihood (CML) methods were specially exploited. For the purpose of achieving copula fitting, the derived rainfall variables by making use of the Standardized Precipitation Index (SPI) were fitted into several distributions. Five copulas, namely Gaussian, Clayton, Frank, Joe and Gumbel were put to the tests to establish the best data fitted copula. The tests produced acknowledged and satisfactory results of copula fitting for rainfall severity and duration. Surveying the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), only three copulas produced a better fit for parametric and semi parametric approaches. Finally, two consistency tests were conducted and the results shown that Frank Copula produced consistent results.
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Chesneau, Christophe. "Theoretical Study of Some Angle Parameter Trigonometric Copulas." Modelling 3, no. 1 (March 10, 2022): 140–63. http://dx.doi.org/10.3390/modelling3010010.
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Copulas are important probabilistic tools to model and interpret the correlations of measures involved in real or experimental phenomena. The versatility of these phenomena implies the need for diverse copulas. In this article, we describe and investigate theoretically new two-dimensional copulas based on trigonometric functions modulated by a tuning angle parameter. The independence copula is, thus, extended in an original manner. Conceptually, the proposed trigonometric copulas are ideal for modeling correlations into periodic, circular, or seasonal phenomena. We examine their qualities, such as various symmetry properties, quadrant dependence properties, possible Archimedean nature, copula ordering, tail dependences, diverse correlations (medial, Spearman, and Kendall), and two-dimensional distribution generation. The proposed copulas are fleshed out in terms of data generation and inference. The theoretical findings are supplemented by some graphical and numerical work. The main results are proved using two-dimensional inequality techniques that can be used for other copula purposes.
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Saminger-Platz, Susanne, Anna Kolesárová, Adam Šeliga, Radko Mesiar, and Erich Peter Klement. "New results on perturbation-based copulas." Dependence Modeling 9, no. 1 (January 1, 2021): 347–73. http://dx.doi.org/10.1515/demo-2021-0116.
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Abstract A prominent example of a perturbation of the bivariate product copula (which characterizes stochastic independence) is the parametric family of Eyraud-Farlie-Gumbel-Morgenstern copulas which allows small dependencies to be modeled. We introduce and discuss several perturbations, some of them perturbing the product copula, while others perturb general copulas. A particularly interesting case is the perturbation of the product based on two functions in one variable where we highlight several special phenomena, e.g., extremal perturbed copulas. The constructions of the perturbations in this paper include three different types of ordinal sums as well as flippings and the survival copula. Some particular relationships to the Markov product and several dependence parameters for the perturbed copulas considered here are also given.
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Shih, Jia-Han, Yoshihiko Konno, Yuan-Tsung Chang, and Takeshi Emura. "Copula-Based Estimation Methods for a Common Mean Vector for Bivariate Meta-Analyses." Symmetry 14, no. 2 (January 18, 2022): 186. http://dx.doi.org/10.3390/sym14020186.
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Traditional bivariate meta-analyses adopt the bivariate normal model. As the bivariate normal distribution produces symmetric dependence, it is not flexible enough to describe the true dependence structure of real meta-analyses. As an alternative to the bivariate normal model, recent papers have adopted “copula” models for bivariate meta-analyses. Copulas consist of both symmetric copulas (e.g., the normal copula) and asymmetric copulas (e.g., the Clayton copula). While copula models are promising, there are only a few studies on copula-based bivariate meta-analysis. Therefore, the goal of this article is to fully develop the methodologies and theories of the copula-based bivariate meta-analysis, specifically for estimating the common mean vector. This work is regarded as a generalization of our previous methodological/theoretical studies under the FGM copula to a broad class of copulas. In addition, we develop a new R package, “CommonMean.Copula”, to implement the proposed methods. Simulations are performed to check the proposed methods. Two real dataset are analyzed for illustration, demonstrating the insufficiency of the bivariate normal model.
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DE BAETS, BERNARD, HANS DE MEYER, and MANUEL ÚBEDA-FLORES. "OPPOSITE DIAGONAL SECTIONS OF QUASI-COPULAS AND COPULAS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17, no. 04 (August 2009): 481–90. http://dx.doi.org/10.1142/s0218488509006108.
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In this paper, we study opposite diagonal sections of quasi-copulas and copulas. The best-possible upper bound for the set of copulas with a given opposite diagonal section being known, we focus on the best-possible lower bound, which in general is a quasi-copula. Moreover, it exhibits an interesting type of bivariate symmetry called opposite symmetry.
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Yang, Jingping, Zhijin Chen, Fang Wang, and Ruodu Wang. "COMPOSITE BERNSTEIN COPULAS." ASTIN Bulletin 45, no. 2 (March 11, 2015): 445–75. http://dx.doi.org/10.1017/asb.2015.1.
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AbstractCopula function has been widely used in insurance and finance for modeling inter-dependency between risks. Inspired by the Bernstein copula put forward by Sancetta and Satchell (2004, Econometric Theory, 20, 535–562), we introduce a new class of multivariate copulas, the composite Bernstein copula, generated from a composition of two copulas. This new class of copula functions is able to capture tail dependence, and it has a reproduction property for the three important dependency structures: comonotonicity, countermonotonicity and independence. We introduce an estimation procedure based on the empirical composite Bernstein copula which incorporates both prior information and data into the estimation. Simulation studies and an empirical study on financial data illustrate the advantages of the empirical composite Bernstein copula estimation method, especially in capturing tail dependence.
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Benkato, Adam, and Christophe Pereira. "An Innovative Copula in Maghrebi Arabic and Its Dialectological Repercussions: The Case of Copular yabda." Languages 6, no. 4 (October 26, 2021): 178. http://dx.doi.org/10.3390/languages6040178.
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Research on copulas in Arabic dialects has hitherto largely focused on the pronominal copula, and has also mostly ignored Maghrebi dialects. Drawing on published literature as well as fieldwork-based corpora, this article identifies and analyzes a hitherto undescribed verbal copula in dialects of Tunisian and northwestern Libya deriving from the verb yabda (“to begin”). We show that copular yabda occurs mostly in predicational copular sentences, with time reference including the habitual present and generic future. It takes nominal, adjectival, and locational predicate types. We also argue for broader inclusion of syntactic isoglosses in Arabic dialectology, and show how copular yabda crosses the traditional isogloss lines established on the basis of phonology, morphology, or lexicon, and therefore contradicts established dialect classifications such as Bedouin/sedentary or Tunisian/Libyan.
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AL-Adilee, Ahmed, Zainalabideen Samad, and Samer Al-Shibley. "Copulas in Classical Probability Sense." Baghdad Science Journal 17, no. 3 (September 1, 2020): 0889. http://dx.doi.org/10.21123/bsj.2020.17.3.0889.
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Copulas are simply equivalent structures to joint distribution functions. Then, we propose modified structures that depend on classical probability space and concepts with respect to copulas. Copulas have been presented in equivalent probability measure forms to the classical forms in order to examine any possible modern probabilistic relations. A probability of events was demonstrated as elements of copulas instead of random variables with a knowledge that each probability of an event belongs to [0,1]. Also, some probabilistic constructions have been shown within independent, and conditional probability concepts. A Bay's probability relation and its properties were discussed with respect to copulas. Moreover, an extension of multivariate constructions of each probabilistic copula has been presented. Finally, we have shown some examples that explain each relation of copula in terms of probability space instead of distribution functions.
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Li, Zhanling, Quanxi Shao, Qingyun Tian, and Louie Zhang. "Copula-based drought severity-area-frequency curve and its uncertainty, a case study of Heihe River basin, China." Hydrology Research 51, no. 5 (May 6, 2020): 867–81. http://dx.doi.org/10.2166/nh.2020.173.
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Abstract Copulas are appropriate tools in drought frequency analysis. However, uncertainties originating from copulas in such frequency analysis have not received significant consideration. This study aims to develop a drought severity-areal extent-frequency (SAF) curve with copula theory and to evaluate the uncertainties in the curve. Three uncertainty sources are considered: different copula functions, copula parameter estimations, and copula input data. A case study in Heihe River basin in China is used as an example to illustrate the proposed approach. Results show that: (1) the dependence structure of drought severity and areal extent can be modeled well by Gumbel; Clayton and Frank depart the most from Gumbel in estimating drought SAF curves; (2) both copula parameter estimation and copula input data contribute to the uncertainties of SAF curves; uncertainty ranges associated with copula input data present wider than those associated with parameter estimations; (3) with the conditional probability decreasing, the differences in the curves derived from different copulas are increasing, and uncertainty ranges of the curves caused by copula parameter estimation and copula input data are also increasing. These results highlight the importance of uncertainty analysis of copula application, given that most studies in hydrology and climatology use copulas for extreme analysis.
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Helgestad Tombleson, Anette. "The copula system of Tawang Monpa." Linguistics of the Tibeto-Burman Area 43, no. 1 (August 28, 2020): 37–54. http://dx.doi.org/10.1075/ltba.17013.tom.
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Abstract This paper is a description of the copula system of Tawang Monpa [Dakpa], an East-Bodish language, spoken in Arunachal Pradesh in India and by small groups of speakers in Bhutan and Tibet. There are two equative copulas in Tawang Monpa: personal jin and neutral jim, and three existential copulas: testimonial ni, neutral num and personal nou. In addition, there are separate negative copulas; equative: personal men and neutral menum, and existential: testimonial mon, neutral munum and personal monou. There is also one example of a past positive copula ne and a past negative copula monelu.
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Kelner, Moshe, Zinoviy Landsman, and Udi E. Makov. "Compound Archimedean Copulas." International Journal of Statistics and Probability 10, no. 3 (April 24, 2021): 126. http://dx.doi.org/10.5539/ijsp.v10n3p126.
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The copula function is an effective and elegant tool useful for modeling dependence between random variables. Among the many families of this function, one of the most prominent family of copula is the Archimedean family, which has its unique structure and features. Most of the copula functions in this family have only a single dependence parameter which limits the scope of the dependence structure. In this paper we modify the generator of Archimedean copulas in a way which maintains membership in the family while increasing the number of dependence parameters and, consequently, creating new copulas having more flexible dependence structure.
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Van Wettere, Niek. "Copularity of French and Dutch (semi-)copular constructions: a behavioral profile analysis." Linguistics 59, no. 6 (October 12, 2021): 1359–88. http://dx.doi.org/10.1515/ling-2021-0160.
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Abstract This study aims to characterize prototypical copularity in contrast with semi-copulas based on probabilistic distributional traits, which indicate preferential associations rather than absolute restrictions. This evaluation of prototypical copularity will be based on a set of 15 French and Dutch copular verbs. A behavioral profile analysis, involving multiple clustering procedures, will demonstrate that (i) prototypical copulas and semi-copulas are never clustered together in one group and that (ii) the group of prototypical copulas is more homogeneous in comparison with the groups of semi-copulas. Next, the bipartition [prototypical copulas vs. semi-copulas] is examined by means of a Firth logistic regression. Overall, it is shown for both French and Dutch that the pattern [(in)animate subject + prepositional SC] is clearly associated with the semi-copulas, whereas the pattern [inanimate subject + nominal SC] is the most distinctive for the prototypical copulas.
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Pustet, Regina. "Copulas in Sgaw Karen." Studies in Language 26, no. 3 (November 1, 2002): 595–612. http://dx.doi.org/10.1075/sl.26.3.05pus.
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Many languages have copula systems involving more than one copula. In such languages, the functional scopes of the participating copulas vary. This kind of typological variation has not yet been studied in great detail. In Sgaw Karen, three copulas exist, and the functional differences among these can be defined at the semantic as well as at the pragmatic level. For instance, the contrast between the copulas mewæþ and kʔ seems to be coextensive with the notional difference between nouns and adjectives as postulated by theorists such as Croft, Langacker, and Wierzbicka.
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Chesneau, Christophe. "On two new modified tawn copulas." Model Assisted Statistics and Applications 19, no. 1 (March 14, 2024): 35–48. http://dx.doi.org/10.3233/mas-231451.
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At its core, copula theory focuses on constructing a copula function, which characterizes the structure of dependence between random variables. In particular, the creation of extreme value copulas is crucial because they allow accurate modeling of extreme dependence that traditional copulas can ignore. In this article, we propose theoretical developments on this subject by proposing two new extreme value copulas. They aim to extend the functionalities of the so-called Tawn copula. This is of interest because the Tawn copula is known to be a powerful tool in modeling joint distributions, particularly in capturing asymmetric and upper tail dependences, making it valuable for analyzing extreme events and tail risk. The proposed copulas are designed to go beyond these attractive features. On the mathematical side, they are derived from new Pickands dependence functions; one modifies the Pickands dependence function of the Tawn copula by using a polynomial-exponential function, and the other does the same but by introducing a power function. The proofs are based on diverse differentiation, arrangement, and inequality techniques. Overall, the created copulas are attractive because (i) they possess modulable levels of asymmetry, (ii) they depend on several tuning parameters, making them very flexible in terms of upper tail dependence in particular, and (iii) they benefit from interesting correlation ranges of values. Several figures and value tables support the theoretical findings.
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González-López, Verónica Andrea, and Vinícius Litvinoff Justus. "A method for the elicitation of copulas." 4open 6 (2023): 2. http://dx.doi.org/10.1051/fopen/2023001.
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In this paper, we introduce a method to construct copulas. The method is based on combining the partial derivatives of two copulas. We prove that the proposed method provides a copula. Then, we exemplify the application of the method in several cases, illustrating the versatility of the method. We also prove that using copulas from the family introduced in Rodríguez-Lallena and Úbeda-Flores (2004) [Stat Probab Lett 66, 3, 315–325. https://doi.org/10.1016/j.spl.2003.09.010], the method provides a copula inside that family.
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Chesneau, Christophe. "A Collection of New Trigonometric- and Hyperbolic-FGM-Type Copulas." AppliedMath 3, no. 1 (March 3, 2023): 147–74. http://dx.doi.org/10.3390/appliedmath3010010.
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Copula analysis was created to explain the dependence of two or more quantitative variables. Due to the need for in-depth data analysis involving complex variable relationships, there is always a need for new copula models with original features. As a modern example, for the analysis of circular or periodic data types, trigonometric copulas are particularly attractive and recommended. This is, however, an underexploited topic. In this article, we propose a new collection of eight trigonometric and hyperbolic copulas, four based on the sine function and the others on the tangent function, all derived from the construction of the famous Farlie–Gumbel–Morgenstern copula. In addition to their original trigonometric and hyperbolic functionalities, the proposed copulas have the feature of depending on three parameters with complementary roles: one is a dependence parameter; one is a shape parameter; and the last can be viewed as an angle parameter. In our main findings, for each of the eight copulas, we determine a wide range of admissible values for these parameters. Subsequently, the capabilities, features, and functions of the new copulas are thoroughly examined. The shapes of the main functions of some copulas are illustrated graphically. Theoretically, symmetry in general, stochastic dominance, quadrant dependence, tail dependence, Archimedean nature, correlation measures, and inference on the parameters are investigated. Some copula shapes are illustrated with the help of figures. On the other hand, some two-dimensional inequalities are established and may be of separate interest.
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Chesneau, Christophe. "Theoretical Validation of New Two-Dimensional One-Variable-Power Copulas." Axioms 12, no. 4 (April 18, 2023): 392. http://dx.doi.org/10.3390/axioms12040392.
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One of the most effective ways to illustrate the relationship between two quantitative variables is to describe the corresponding two-dimensional copula. This approach is acknowledged as practical, nonredundant, and computationally manageable in the context of data analysis. Modern data, however, contain a wide variety of dependent structures, and the copulas now in use may not provide the best model for all of them. As a result, researchers seek to innovate by building novel copulas with appealing properties that are also based on original methodologies. The foundations are theoretical; for a copula to be validated, it must meet specific requirements, which frequently dictate the constraints that must be placed on the relevant parameters. In this article, we make a contribution to the understudied field of one-variable-power copulas. We first identify the specific assumptions that, in theory, validate copulas of such nature. Some other general copulas and inequalities are discussed. Our general results are illustrated with numerous examples depending on two or three parameters. We also prove that strong connections exist between our assumptions and well-established distributions. To highlight the importance of our findings, we emphasize a particular two-parameter, one-variable-power copula that unifies the definition of some other copulas. We reveal its versatile shapes, related functions, various symmetry, Archimedean nature, geometric invariance, copula ordering, quadrant dependence, tail dependence, correlations, and distribution generation. Numerical tables and graphics are produced to support some of these properties. The estimation of the parameters based on data is discussed. As a complementary contribution, two new, intriguing one-variable-power copulas beyond the considered general form are finally presented and studied.
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Shchetinin, Eugeny Yu. "Vine copulas structures modeling on Russian stock market." Discrete and Continuous Models and Applied Computational Science 27, no. 4 (December 15, 2019): 343–54. http://dx.doi.org/10.22363/2658-4670-2019-27-4-343-354.
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Pair-copula constructions have proven to be a useful tool in statistical modeling, particularly in the field of finance. The copula-based approach can be used to choose a model that describes the dependence structure and marginal behaviour of the data in efficient way, but is usually applied to pairs of securities. In contrast, vine copulas provide greater flexibility and permit the modeling of complex dependency patterns using the rich variety of bivariate copulas which may be arranged and analysed in a tree structure. However, the number of possible configurations of a vine copula grows exponentially as the number of variables increases, making model selection a major challenge in development. So, to learn the best possible model, one has to identify the best possible structure, which necessitates identifying the connections between the variables and selecting between the multiple bivariate copulas for each pair in the structure. This paper features the use of regular vine copulas in analysis of the co-dependencies of four major Russian Stock Market securities such as Gazprom, Sberbank, Rosneft and FGC UES, represented by the RTS index. For these stocks the D-vine structures of bivariate copulas were constructed, which models are described by Gumbel, Student, BB1and BB7 copulas, and estimates of their parameters were obtained. Computer simulations showed a high accuracy of the approximation of the explored data by D-vine structure of bivariate copulas and the effectiveness of our approach in general.
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Aldhufairi, Fadal Abdullah Ali, and Jungsywan H. Sepanski. "New Bivariate Copulas via Lomax Distribution Generated Distortions." AppliedMath 4, no. 2 (May 17, 2024): 641–65. http://dx.doi.org/10.3390/appliedmath4020035.
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We develop a framework for creating distortion functions that are used to construct new bivariate copulas. It is achieved by transforming non-negative random variables with Lomax-related distributions. In this paper, we apply the distortions to the base copulas of independence, Clayton, Frank, and Gumbel copulas. The properties of the tail dependence coefficient, tail order, and concordance ordering are explored for the new families of distorted copulas. We conducted an empirical study using the daily net returns of Amazon and Google stocks from January 2014 to December 2023. We compared the popular Clayton, Gumbel, Frank, and Gaussian copula models to their corresponding distorted copula models induced by the unit-Lomax and unit-inverse Pareto distortions. The new families of distortion copulas are equipped with additional parameters inherent in the distortion function, providing more flexibility, and are demonstrated to perform better than the base copulas. After analyzing the data, we have found that the joint extremes of Amazon and Google stocks are more likely for high daily net returns than for low daily net returns.
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Geist, Ljudmila. "Russisch byt' ('sein') als funktionale und/oder lexikalische Kategorie." ZAS Papers in Linguistics 14 (January 1, 1999): 1–39. http://dx.doi.org/10.21248/zaspil.14.1999.3.
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The present study offers an analysis of the Russian copular constructions with predicate nominals. In such copular sentences two cases may mark the predicate: the nominative and the instrumental as in 'Anna byla medsestra/medsestroj' - 'Anna was-3sg.fem.a nursenom/instr'. In the present tense the copula has a null-form and the predicate nominal can only be in the nominative. I argue that the case alternation corresponds to the distinction of Stage Level and Individual Level Predicates in the sense of Kratzer (1994) and Diesing (1992), but with some objections. The copula with Instrumental forms S-Predicates, which are analyzed as predicates applying to situations referring to time. The copula with nominative forms I-Predicates, which attribute properties to individuals without referring to time. I-Predicates have no situation argument. Data that show the (in-)compatibility of copular sentences with certain spatial or temporal modifiers provide a reason to assume a situation argument in byt' + Instr but not in byt' + Nom.
Byt' behaves differently in different grammatical contexts: in contexts of sentence negation, yes/no-questions and under focus byt' + Instr behaves like a lexical category, while byt' + Nom behaves like a functional category. As a functional category byt' + Nom is non-overt in the present and is always finite. The semantic distinction between nominative and instrumental predicate NPs is pegged to an opposition between a structure with a functional copula as the only tense and agreement marker with base position in TP and a lexical copula in VP (Franks 1995, Bailyn&Rubin 1991). To explain phenomena of the copula in Russian I propose an integrated syntactic model for two copulas. The two copulas may be conceived as distinct realizations of one verbal lexical entry which will be specified as a lexical or as functional category in the course of lexical insertion. The Model of Parallel Morphology might be used to explain this phenomenon.
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Pfeifer, Dietmar, Andreas Mändle, Olena Ragulina, and Côme Girschig. "New copulas based on general partitions-of-unity (part III) — the continuous case." Dependence Modeling 7, no. 1 (June 28, 2019): 181–201. http://dx.doi.org/10.1515/demo-2019-0009.
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AbstractIn this paper we discuss a natural extension of infinite discrete partition-of-unity copulas which were recently introduced in the literature to continuous partition of copulas with possible applications in risk management and other fields. We present a general simple algorithm to generate such copulas on the basis of the empirical copula from high-dimensional data sets. In particular, our constructions also allow for an implementation of positive tail dependence which sometimes is a desirable property of copula modelling, in particular for internal models under Solvency II.
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Kujath, Elizabeth, and Jenneke van der Wal. "Copular constructions in Makhuwa‑Enahara." Linguistics in the Netherlands 40 (November 3, 2023): 155–77. http://dx.doi.org/10.1075/avt.00085.kuj.
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Abstract This paper describes the possible predication strategies in Makhuwa-Enahara and under what circumstances each occurs. Makhuwa-Enahara (Bantu P31E) has three main copular constructions: Predicative Lowering, the invariant copulas ti (affirmative) and kahi (negative), and the verbal copulas ori and okhala. It was previously posited that the choice between predication strategies depended on the syntactic type of the predicate, but further analysis shows that deference is instead given to the semantic type of the predication. The underlying structures of Makhuwa-Enahara are identical for Equation, Predication, and Identification; Specification shows a different structure, and Locative predication yet another. Predicative Lowering and the invariant copula are argued to be different spell-outs of the Pred head, depending on its raised position within the syntactic tree and whether or not the initial element of the predicate is long enough to undergo Predicative Lowering.
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Bacigál, Tomáš, and Mária Ždímalová. "Convergence of Linear Approximation of Archimedean Generator from Williamson’s Transform in Examples." Tatra Mountains Mathematical Publications 69, no. 1 (June 27, 2017): 1–18. http://dx.doi.org/10.1515/tmmp-2017-0010.
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Abstract We discuss a new construction method for obtaining additive generators of Archimedean copulas proposed by McNeil, A. J.-Nešlehová, J.: Multivariate Archimedean copulas, d-monotone functions and l1-norm symmetric distributions, Ann. Statist. 37 (2009), 3059-3097, the so-called Williamson n-transform, and illustrate it by several examples. We show that due to the equivalence of convergences of positive distance functions, additive generators and copulas, we may approximate any n-dimensional Archimedean copula by an Archimedean copula generated by a transformation of weighted sum of Dirac functions concentrated in certain suitable points. Specifically, in two dimensional case this means that any Archimedean copula can be approximated by a piece-wise linear Archimedean copula, moreover the approximation of generator by linear splines circumvents the problem with the non-existence of explicit inverse.
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Ahn, Jae Youn, and Sebastian Fuchs. "On Minimal Copulas under the Concordance Order." Journal of Optimization Theory and Applications 184, no. 3 (December 10, 2019): 762–80. http://dx.doi.org/10.1007/s10957-019-01618-4.
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AbstractIn the present paper, we study extreme negative dependence focussing on the concordance order for copulas. With the absence of a least element for dimensions $$d\ge 3$$d≥3, the set of all minimal elements in the collection of all copulas turns out to be a natural and quite important extreme negative dependence concept. We investigate several sufficient conditions, and we provide a necessary condition for a copula to be minimal. The sufficient conditions are related to the extreme negative dependence concept of d-countermonotonicity and the necessary condition is related to the collection of all copulas minimizing multivariate Kendall’s tau. The concept of minimal copulas has already been proved to be useful in various continuous and concordance order preserving optimization problems including variance minimization and the detection of lower bounds for certain measures of concordance. We substantiate this key role of minimal copulas by showing that every continuous and concordance order preserving functional on copulas is minimized by some minimal copula, and, in the case the continuous functional is even strictly concordance order preserving, it is minimized by minimal copulas only. Applying the above results, we may conclude that every minimizer of Spearman’s rho is also a minimizer of Kendall’s tau.
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Budiarti, Retno, Kumala Intansari, I. Gusti Putu Purnaba, and Fendy Septyanto. "Modelling Dependencies of Stock Indices During Covid-19 Pandemic by Extreme-Value Copula." JTAM (Jurnal Teori dan Aplikasi Matematika) 7, no. 3 (July 17, 2023): 805. http://dx.doi.org/10.31764/jtam.v7i3.15109.
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Quantifying dependence among variables is the core of all modelling efforts in financial models. In the recent years, copula was introduced to model the dependence structure among financial assets return, and its application developed fast. A large number of studies on copula have been performed, but the study of multivariate extremes related with copulas was quite behind in comparison with the research on copulas. The COVID-19 pandemic is an extreme event that has caused the collapse of various economic activities which resulted in the decline of stock prices. The modelling of extreme events is therefore important to mitigate huge financial losses. Extreme-value copula can be suitable to quantify dependencies among assets under an extreme event. In this paper, we study the modelling of extreme value dependence using extreme value copulas on finance data. This model was applied in the portfolio of the IDX Composite Index (IHSG), Straits Times Index (STI) and Kuala Lumpur Stock Exchange (KLSE). Each individual asset return is modelled by the ARMA-GARCH and the joint distribution is modelled using extreme value copulas. This empirical study showed that Gumbel copula is the most appropriate extreme value copulas for the three indices. The results of this study are expected to be used as a basis for investors in the formation of a portfolio consisting of 2 financial assets and a portfolio consisting of 3 financial assets.
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Bernard, Carole, Xiao Jiang, and Steven Vanduffel. "A Note on ‘Improved Fréchet Bounds and Model-Free Pricing of Multi-Asset Options’ by Tankov (2011)." Journal of Applied Probability 49, no. 3 (September 2012): 866–75. http://dx.doi.org/10.1239/jap/1346955339.
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Tankov (2011) improved the Fréchet bounds for a bivariate copula when its values on a compact subset of [0, 1]2 are given. He showed that the best possible bounds are quasi-copulas and gave a sufficient condition for these bounds to be copulas. In this note we give weaker sufficient conditions to ensure that the bounds are copulas. We also show how this can be useful in portfolio selection. It turns out that finding a copula as a lower bound plays a key role in determining optimal investment strategies explicitly for investors with some type of state-dependent constraints.
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Bernard, Carole, Xiao Jiang, and Steven Vanduffel. "A Note on ‘Improved Fréchet Bounds and Model-Free Pricing of Multi-Asset Options’ by Tankov (2011)." Journal of Applied Probability 49, no. 03 (September 2012): 866–75. http://dx.doi.org/10.1017/s0021900200009591.
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Tankov (2011) improved the Fréchet bounds for a bivariate copula when its values on a compact subset of [0, 1]2 are given. He showed that the best possible bounds are quasi-copulas and gave a sufficient condition for these bounds to be copulas. In this note we give weaker sufficient conditions to ensure that the bounds are copulas. We also show how this can be useful in portfolio selection. It turns out that finding a copula as a lower bound plays a key role in determining optimal investment strategies explicitly for investors with some type of state-dependent constraints.
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Cooray, Kahadawala. "Strictly Archimedean copulas with complete association for multivariate dependence based on the Clayton family." Dependence Modeling 6, no. 1 (February 7, 2018): 1–18. http://dx.doi.org/10.1515/demo-2018-0001.
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Abstract The family of Clayton copulas is one of the most widely used Archimedean copulas for dependency measurement. A major drawback of this copula is that when it accounts for negative dependence, the copula is nonstrict and its support is dependent on the parameter. The main motivation for this paper is to address this drawback by introducing a new two-parameter family of strict Archimedean copulas to measure exchangeable multivariate dependence. Closed-form formulas for both complete and d−monotonicity parameter regions of the generator and the copula distribution function are derived. In addition, recursive formulas for both copula and radial densities are obtained. Simulation studies are conducted to assess the performance of the maximum likelihood estimators of d−variate copula under known marginals. Furthermore, derivativefree closed-form formulas for Kendall’s distribution function are derived. A real multivariate data example is provided to illustrate the flexibility of the new copula for negative association.
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Geenens, Gery. "Copula modeling for discrete random vectors." Dependence Modeling 8, no. 1 (January 1, 2020): 417–40. http://dx.doi.org/10.1515/demo-2020-0022.
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Abstract Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Sklar’s theorem, “the fundamental theorem of copulas”, makes a clear distinction between the continuous case and the discrete case, though. In particular, the copula of a discrete random vector is not fully identifiable, which causes serious inconsistencies. In spite of this, downplaying statements may be found in the related literature, where copula methods are used for modelling dependence between discrete variables. This paper calls to reconsidering the soundness of copula modelling for discrete data. It suggests a more fundamental construction which allows copula ideas to smoothly carry over to the discrete case. Actually it is an attempt at rejuvenating some century-old ideas of Udny Yule, who mentioned a similar construction a long time before copulas got in fashion.
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Lundy, Arnhilda Aspasia, Mila Novita, and Ida Fithriani. "MODELING THE BENEFITS OF A MARRIAGE REVERSE ANNUITY CONTRACT WITH DEPENDENCY ASSUMPTIONS USING ARCHIMEDEAN COPULA." BAREKENG: Jurnal Ilmu Matematika dan Terapan 18, no. 4 (October 11, 2024): 2137–52. http://dx.doi.org/10.30598/barekengvol18iss4pp2137-2152.
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Social security benefits may not be enough for retirement. Equity release products like marriage reverse annuities can boost retirement income for older couples. Marriage reverse annuity’s contract convert all or part of the real estate value of elderly spouses while they are living (joint life status) or after one partner dies (last survivor status). Since husband and wife face the same death risk, the chance of death between spouses is believed to be dependent for realism. Thus, copula models the future dependency model of a husband and wife. Sklar's theorem states that copulas link bivariate distribution and marginal cumulative functions. One of the most common copulas is Archimedean copula. Clayton, Gumbel, and Frank are Archimedean copula that will be used in this investigation. The Indonesian Mortality Table IV data is used to obtain the marginal distribution of the male and female which will then be used to construct copulas (Clayton, Gumbel, and Frank) that combine two marginal distributions into a joint distribution. The marginal distribution of Indonesian Mortality Table IV is uncertain, hence Canonical Maximum Likelihood parameter estimation is utilized to estimate the parameter of copulas. Multiple-state models depict the marriage reverse annuity model for joint life and last survivor status. The probability structure is based on Sklar's theorem and copula survival function. The contract benefits calculation utilizing copulas (Clayton, Gumbel, and Frank) shows that joint life status benefits are higher than last survivor status. Joint life status uses the dependence assumption with Frank's copula to calculate the smallest annual benefit value of a marriage reverse annuity contract, while last survivor status uses the independence assumption (without copula).
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Chesneau, Christophe. "A study of the power-cosine copula." Open Journal of Mathematical Analysis 5, no. 1 (June 29, 2021): 85–97. http://dx.doi.org/10.30538/psrp-oma2021.0086.
Full textAbstract:
Copulas played a key role in numerous areas of statistics over the last few decades. In this paper, we offer a new kind of trigonometric bivariate copula based on power and cosine functions. We present it via analytical and graphical approaches. We show that it may be used to create a new bivariate normal distribution with interesting shapes. Subsequently, the simplest version of the suggested copula is highlighted. We discuss some of its relationships with the Farlie-Gumbel-Morgensten and simple polynomial-sine copulas, establish that it is a member of a well-known semi-parametric family of copulas, investigate its dependence domains, and show that it has no tail dependence.
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El Ktaibi, Farid, Rachid Bentoumi, and Mhamed Mesfioui. "On the Ratio-Type Family of Copulas." Mathematics 12, no. 11 (June 3, 2024): 1743. http://dx.doi.org/10.3390/math12111743.
Full textAbstract:
Investigating dependence structures across various fields holds paramount importance. Consequently, the creation of new copula families plays a crucial role in developing more flexible stochastic models that address the limitations of traditional and sometimes impractical assumptions. The present article derives some reasonable conditions for validating a copula of the ratio-type form uv/(1−θf(u)g(v)). It includes numerous examples and discusses the admissible range of parameter θ, showcasing the diversity of copulas generated through this framework, such as Archimedean, non-Archimedean, positive dependent, and negative dependent copulas. The exploration extends to the upper bound of a general family of copulas, uv/(1−θϕ(u,v)), and important properties of the copula are discussed, including singularity, measures of association, tail dependence, and monotonicity. Furthermore, an extensive simulation study is presented, comparing the performance of three different estimators based on maximum likelihood, ρ−inversion, and the moment copula method.