Some new results on convolutions of heterogeneous gamma random variables

SOME RESULTS OF MOMENTS OF UNCERTAIN RANDOM VARIABLES

Chance theory is a mathematical methodology for dealing with indeterminatephenomena including uncertainty and randomness.Consequently, uncertain random variable is developed to describe the phenomena which involveuncertainty and randomness.Thus, uncertain random variable is a fundamental concept in chance theory.This paper provides some practical quantities to describe uncertain random variable...

Schur properties of convolutions of gamma random variables

Sufficient conditions for comparing the convolutions of heterogeneousgamma random variables in terms of the usual stochastic order are established.Such comparisons are characterized by the Schur convexity properties of thecumulative distribution function of the convolutions. Some examples of thepractical applications of our results are given.

Some Unified Results on Comparing Linear Combinations of Independent Gamma Random Variables

SOME PROBABILISTIC INEQUALITIES FOR FUZZY RANDOM VARIABLES

In this paper, the concepts of positive dependence and linearlypositive quadrant dependence are introduced for fuzzy random variables. Also,an inequality is obtained for partial sums of linearly positive quadrant depen-dent fuzzy random variables. Moreover, a weak law of large numbers is estab-lished for linearly positive quadrant dependent fuzzy random variables. Weextend some well known inequ...

On Some Arithmetic Convolutions

0. Introduction. In this paper we first review some of the known arithmetical convolutions with particular reference to a class of convolutions which may be called Lehmer's ~-products. These products are general enough to include as special cases the well known Dirichlet and unitary products and other Narkiewicz-type products. We indicate a few new cases of ~-products, and in particular study i...