Abstract In our previous work, we have extended the classical notion of increasing convex stochastic dominance relation with respect to a probability to the more general case of a normalized monotone (but not necessarily additive) set function, also called a capacity. In the present paper, we...

In the present paper, we introduce a quantile based Rényi’s entropy function and its residual version. We study certain properties and applications of the measure. Unlike the residual Rényi’s entropy function, the quantile version uniquely determines the distribution.

The total time on test transform has been used in reliability to compare two random lifetimes. Despite that it has been used widely in this context, it is not very clear in which sense the random variables are being compared. In this paper we provide a characterization which reveals the true...

Motivated by too restrictive or even incorrect statements about generalized inverses in the literature, properties about these functions are investigated and proven. Examples and counterexamples show the importance of generalized inverses in mathematical theory and its applications. Copyright...

Motivated by too restrictive or even incorrect statements about generalized inverses in the literature, properties about these functions are investigated and proven. Examples and counterexamples show the importance of generalized inverses in mathematical theory and its applications. Copyright...

It is well-known, in the literature, that most of the characterization results on exponential distribution are based on the solution of Cauchy functional equation and integrated Cauchy functional equation. In the present paper, we consider the functional equation <Equation ID="Equa"> <EquationSource Format="TEX">$$F(x)=F(xy) + F(xQ(y)), \quad...</equationsource></equation>