A measure of mutual complete dependence in discrete variables through subcopula

A subcopula based dependence measure

a) 0 = FX,Y (−∞, y) = S(FX(−∞), FY (y)) = S(0, v) where v ∈ Ran FY , and analogously S(u, 0) = 0 for u ∈ Ran FX . b) FY (y) = FX,Y (+∞, y) = S(FX(+∞), FY (y)) = S(1, v) where v = FY (y), and analogously S(u, 1) = u where u = FX(x) for some x ∈ R. c) 0 ≤ P (x1 < X ≤ x2 , y1 < Y ≤ y2) = FX,Y (x2, y2)−FX,Y (x2, y1)−FX,Y (x1, y2)+ FX,Y (x1, y1) and therefore by (1) we have that S(u2, v2)− S(u2, v1)...

Mutual Information: a dependence measure for nonlinear time series

This paper investigates the possibility to analyse the structure of unconditional or conditional (and possibly nonlinear) dependence in ...nancial returns without requiring the speci...cation of mean-variance models or a theoretical probability distribution. Abstract The main goal of the paper is to show how mutual information can be used as a measure of dependence in ...nancial time series. On...

A new estimate of mutual information based measure of dependence between two variables: properties and fast implementation

This article proposes a mutual information based dependence measure where the bin length is decided using a function of the maximum separation between points. Some properties of the proposed measure are also discussed. The performance of the proposed measure has been compared with other generally accepted measures like correlation coefficient, distance correlation (dcor), Maximal Information Co...

Mutual Dependence Demands Mutual Sharing

Complete Axiomatization of Discrete-Measure Almost-Everywhere Quantification

Following recent developments in the topic of generalized quantifiers, and also having in mind applications in the areas of security and artificial intelligence, a conservative enrichment of (two-sorted) first-order logic with almost-everywhere quantification is proposed. The completeness of the axiomatization against the measure-theoretic semantics is carried out using a variant of the Lindenb...