Multivariate patchwork copulas: a unified approach with applications to partial comonotonicity

none2siWe present a general view of patchwork constructions of copulas that encompasses previous approaches based on similar ideas (ordinal sums, gluing methods, piecing-together, etc.). Practical applications of the new methodology are connected with the determination of copulas having specified behaviour in the tails, such as upper comonotonic copulas.Durante, Fabrizio; Sánchez, Juan Fernández; Sempi, CarloDurante, Fabrizio; Sánchez, Juan Fernández; Sempi, Carl

Componentwise concave copulas and their asymmetry

summary:The class of componentwise concave copulas is considered, with particular emphasis on its closure under some constructions of copulas (e.g., ordinal sum) and its relations with other classes of copulas characterized by some notions of concavity and/or convexity. Then, a sharp upper bound is given for the $L^{\infty}$-measure of non-exchangeability for copulas belonging to this class

Joint modelling of the body and tail of bivariate data

In situations where both extreme and non-extreme data are of interest, modelling the whole data set accurately is important. In a univariate framework, modelling the bulk and tail of a distribution has been extensively studied before. However, when more than one variable is of concern, models that aim specifically at capturing both regions correctly are scarce in the literature. A dependence model that blends two copulas with different characteristics over the whole range of the data support is proposed. One copula is tailored to the bulk and the other to the tail, with a dynamic weighting function employed to transition smoothly between them. Tail dependence properties are investigated numerically and simulation is used to confirm that the blended model is sufficiently flexible to capture a wide variety of structures. The model is applied to study the dependence between temperature and ozone concentration at two sites in the UK and compared with a single copula fit. The proposed model provides a better, more flexible, fit to the data, and is also capable of capturing complex dependence structures.Comment: 36 pages, 12 figure

solution to an open problem about a transformation on the space of copulas

AbstractWe solve a recent open problem about a new transformation mapping the set of copulas into itself. The obtained mapping is characterized in algebraic terms and some limit results are proved

Social Mobility in Developing Countries

Social mobility is the hope of economic development and the mantra of a good society. There are disagreements about what constitutes social mobility, but there is broad agreement that people should have roughly equal chances of success regardless of their economic status at birth. Concerns about rising inequality have engendered a renewed interest in social mobility—especially in the developing world. However, efforts to construct the databases and meet the standards required for conventional analyses of social mobility are at a preliminary stage and need to be complemented by innovative, conceptual, and methodological advances. If forms of mobility have slowed in the West, then we might be entering an age of rigid stratification with defined boundaries between the always-haves and the never-haves—which does not augur well for social stability. Social mobility research is ongoing, with substantive findings in different disciplines—typically with researchers in isolation from each other. A key contribution of this book is the pulling together of the emerging streams of knowledge. Generating policy-relevant knowledge is a principal concern. Three basic questions frame the study of diverse aspects of social mobility in the book. How to assess the extent of social mobility in a given development context when the datasets by conventional measurement techniques are unavailable? How to identify drivers and inhibitors of social mobility in particular developing country contexts? How to acquire the knowledge required to design interventions to raise social mobility, either by increasing upward mobility or by lowering downward mobility