26 research outputs found

    Characterizations of bivariate conic, extreme value, and Archimax copulas

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    Based on a general construction method by means of bivariate ultramodular copulas we construct, for particular settings, special bivariate conic, extreme value, and Archimax copulas. We also show that the sets of copulas obtained in this way are dense in the sets of all conic, extreme value, and Archimax copulas, respectively

    Aggregation functions with given super-additive and sub-additive transformations

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    Aggregation functions and their transformations have found numerous applications in various kinds of systems as well as in economics and social science. Every aggregation function is known to be bounded above and below by its super-additive and sub-additive transformations. We are interested in the “inverse” problem of whether or not every pair consisting of a super-additive function dominating a sub-additive function comes from some aggregation function in the above sense. Our main results provide a negative answer under mild extra conditions on the super- and sub-additive pair. We also show that our results are, in a sense, best possible

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    Componentwise concave copulas and their asymmetry

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    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 LL^{\infty}-measure of non-exchangeability for copulas belonging to this class

    A Class of Individual Expenditure Functions

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    This study examines the regularity properties ensuring that individual expenditure functions are legitimate individual cost functions in the context of collective household models. The structure of collective household models entails a scaling of income through a function that describes how resources are shared within the household. This modified income function defines expenditure functions at the individual level. Our study completes previous work on modifying functions by Barten, Gorman, and Lewbel that was limited to the investigation of the scaling of prices and the translation of income without considering the scaling of incomes. We find that the product of the modifying function and the household expenditure function maintains the regularity properties of expenditure functions if the modifying function is positive, homogeneous of degree zero and at least quasi-concave. We also examine how changes in prices affect the curvature of the modified income function and, in turn, inequality in the distribution of resources within the household. An example shows how our results can be used to test the curvature properties of individual expenditure functions as well as to measure the inequality within the household
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