7,995 research outputs found
Addendum to "Information Theoretic Interpretation of Forte's Entropy for the Grand Canonical Ensemble"
No full textA comparison is carried out of the upper bounds of the previous paper by the author and that provided by Elias
How many Archimedean copulas are there?
No full textTwo algebraic notions, power of an associative binary function and nilpotency, are used in order to show that every bivariate
Archimedean copula is isomorphic to either the independence copula , if it is strict, or to the lower Fr\'{e}chet--Hoeffding bound , if it is nilpotent
Copulae: some mathematical aspects
No full textThis paper starts with a few critical considerations about the use of copulas in applications, mainly in the field of Mathematical
Finance. Two points will be stressed: (i) the construction of asymmetric copulas and (ii) the construction of multivariate copulas.
Also, it briefly touches on the long-standing problem of compatibility
Why Shannon's Entropy: a Further Reason
No full textProperites of the the conditional entropy are studied and it is shown that Hartley's conditional entropy satisfies a proper subset of the desirable properties; this justifies the adoption of Shannon's entropy
A Counterexample about Lewis' Principle
No full textWe show that in general the density that maximizes the probability density of the entropy functional when its marginal density for a aprticle is assigned does not satisfy the equation of motion appropriate for the complete description of a conservative dynamical system, even in the case in which the probability density is chosen amonmg those that satisfy the reduced equation of motion. This contradicts what is implicitly admitted by Lewis's princiel
A survey of copula-–based measures of association
No full textWe survey the measures of association that are based on bivariate copulas. Almost no proof will be reported, although
an exception is made in the case of the Schweizer--Wolff measure, since the details of the proof are mainly contained in Wolff's Ph.D. dissertation, which is not readily available
Product Topologies on the Space of Distribution Functions
No full textWe study the connection between weak convergence in the space of multiple distribution functions and convergence in the product topology induced on the product by the metrics on these spaces. We show that, for r>1 , weak convergence in is slightly more general than convergence in either product topology on . We also give several sufficient conditions under which these two modes of convergence are equivalent
Two Uniqueness Problems Connected with Lewis' Principle
No full textThe application of Lewis's principle depends on the existence and the uniqueness of the solutions of a certain class of variational problems. We show that in two cases of particular physical interest uniquenes can beestablished in a rigorous manner
Variations on a Theme by Scheffé
No full textUna versione finitamente additiva del classico teorema di Scheffé suggerisce una versione rafforzata dello stesso teorema, nella quale la convergenza q.o. delle densità è sostituita dalla convergenza in misura.We present here a finitely additive version of Scheffé's theorem. This version, in its turn, suggests a strengthened form of the traditional Scheffé1 s theorem, in which convergence a.e. of the densities is replaced by convergence in measure
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