This paper suggests a new technique to construct first order Markov processes using products of copula functions, in the spirit of Darsow et al. (1992). The approach requires the definition of: i) a sequence of distribution functions of the increments of the process; ii) a sequence of copula functions representing dependence between each increment of the process and the corresponding level of t...

Copulas are a general tool for assessing the dependence structure of random variables. Important properties as well as a number of examples are discussed, including Archimedean copulas and the Marshall-Olkin copula. As measures of the dependence we consider linear correlation, rank correlation, the coefficients of tail dependence and association. Copulas are a tool for modeling and capturing th...

Droughts produce a complex set of negative economic, environmental, and social impacts across a country or region. Using monthly standardized Precipitation Index (SPI) values, drought characteristics, namely, drought duration, severity, interval time and minimum SPI values, were determined. Two exponential distributions were used to model drought duration and interval time, respectively; gamma ...

Aggregation operators transform a finite number of inputs, called arguments, into a single output. They are applied in many theoretical and practical domains and in particular aggregation operators play important role in different approaches to decision making, where values to be aggregated are typically preference or satisfaction degrees. Many operators of different type have been considered i...

In recent years copulas turned out to be a promising tool in multivariate modelling, mostly with applications in actuarial sciences and hydrology. In short, copula is a function which allows modelling dependence structure between stochastic variables. The main advantage is that the copula approach can split the problem of constructing multivariate probability distributions into a part containin...

Multivariate exchangeable Archimedean copulas are one of the most popular classes of copulas that are used in actuarial science and finance for modelling risk dependencies and for using them to quantify the magnitude of tail dependence. Owing to the increase in popularity of copulas to measure dependent risks, generating multivariate copulas has become a very crucial exercise. Current methods f...

Copulas recently emerged in many data analysis and knowledge discovery tasks as a flexible tool for modeling complex multivariate distributions. The paper presents a method for estimating copulas from one of the most popular classes of copulas, namely hierarchical Archimedean copulas. The method is based on the close relationship of the copula structure and the values of Kendall’s tau computed ...

In this paper we propose a clustering procedure aimed at grouping time series with an association between extremely low values, measured by the lower tail dependence coefficient. Firstly, we estimate the coefficient using an Archimedean copula function. Then, we propose a dissimilarity measure based on tail dependence coefficients and a two-step procedure to be used with clustering algorithms w...