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...

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>

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...

Di Crescenzo and Longobardi (2002) introduced a measure of uncertainty in past lifetime distributions and studied its relationship with residual entropy function. In the present paper, we introduce a quantile version of the entropy function in past lifetime and study its properties. Unlike the...

Graphing univariate distributions is central to both statistical graphics, in general, and StataÕs graphics, in particular. Now that Stata 8 is out, a review of official and user-written commands is timely. The emphasis here is on going beyond what is obviously and readily available, with...

The right truncated Gini index and mean difference are useful tools in the analysis of incomes and the left truncated versions of these functions can be employed in reliability modelling. In this paper we identify the distributions characterized by simple functional forms of these measures and...

We study a five-parameter lifetime distribution called the McDonald extended exponential model to generalize the exponential, generalized exponential, Kumaraswamy exponential and beta exponential distributions, among others. We obtain explicit expressions for the moments and incomplete moments,...

It has been commonly admitted that the meaning of a descriptive feature of distributions is given by an ordering and that the measures for this feature are meaningful only if they preserve the ordering. However, while many multivariate kurtosis measures have been introduced, multivariate...