Causal Strength via Shannon Capacity: Axioms, Estimators and Applications

Conditional Dependence via Shannon Capacity: Axioms, Estimators and Applications

We consider axiomatically the problem of estimating the strength of a conditional dependence relationship PY |X from a random variables X to a random variable Y . This has applications in determining the strength of a known causal relationship, where the strength depends only on the conditional distribution of the effect given the cause (and not on the driving distribution of the cause). Shanno...

On the Estimation of Shannon Entropy

Shannon entropy is increasingly used in many applications. In this article, an estimator of the entropy of a continuous random variable is proposed. Consistency and scale invariance of variance and mean squared error of the proposed estimator is proved and then comparisons are made with Vasicek's (1976), van Es (1992), Ebrahimi et al. (1994) and Correa (1995) entropy estimators. A simulation st...

BASE AXIOMS AND SUBBASE AXIOMS IN M-FUZZIFYING CONVEX SPACES

Based on a completely distributive lattice $M$, base axioms and subbase axioms are introduced in $M$-fuzzifying convex spaces. It is shown that a mapping $mathscr{B}$ (resp. $varphi$) with the base axioms (resp. subbase axioms) can induce a unique $M$-fuzzifying convex structure with  $mathscr{B}$ (resp. $varphi$) as its base (resp. subbase). As applications, it is proved that bases and subbase...

Some separation axioms via modified θ-open sets

Stress-Strength and Ageing Intensity Analysis via a New Bivariate Negative Gompertz-Makeham Model

In Demography and modelling mortality (or failure) data the univariate Makeham-Gompertz is well-known for its extension of exponential distribution. Here, a bivariate class of Gompertz--Makeham distribution is constructed based on random number of extremal events. Some reliability properties such as ageing intensity, stress-strength based on competing risks are given. Also dependence properties...