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For a large class of distribution functions we study properties of the product of random variables X and Y. We take into account the dependency structure between X and Y by making assumptions about the asymptotic equality P(X > x|Y = y) ~ h(y)P(X > x) as x [right arrow] [infinity], uniformly for y in the range of Y. As particular consequences, some well-known results concerning the product of random variables are reviewed, among them the Breiman's theorem. An application is made in the case where the dependence between X and Y is characterized by asymptotic conditions on their copula., 1. Introduction The product of two random variables (r.vs) X and Y occurs frequently in many phenomena, such as in risk theory, where such products arise naturally when insured or [...]

We introduce different types of multivariate regularly varying functions and define a new class of positive and measurable functions that are bounded between such multivariate Karamata functions. We study integrals and Laplace transforms of these functions. We use the results to study the tail of convolutions of bivariate distribution functions., 1. Introduction Recently Cadena et al. [2-4] introduced and studied the class of positive and measurable functions, such that [lim.sub.x[right arrow][infinity]] log U(x)/log x = [rho], a finite real number. [...]

We define a new class of positive and measurable functions that are bounded by regularly varying functions (which were introduced by Karamata). We study integrals and Laplace transforms of these functions. We use the obtained results to study the tail of convolutions of distribution functions. The results are extended to functions that are bounded by O-regularly varying functions., 1. Introduction Recently Cadena et al. (see [2-4]) introduced and studied the class M([rho]) of positive and measurable functions U with support [R.sup.+], bounded on finite intervals, such that [mathematical [...]

In the paper we present a simple game that students can play in the classroom. The game can be used to show that random variables can behave in an unexpected way: the expected mean can tend to zero or to infinity; the variance can tend to zero or to infinity. The game can also be used to introduce the lognormal distribution. (Contains 1 table and 1 figure.)

The article reports on the subexponential distribution functions in Rd. It discusses the univariate subexponential distributions, multivariate subexponential distributions and others. It also discusses the asymptotic behavior of the sums wherein it denotes probability distribution.

The article reports on the subexponential distribution functions in Rd. It discusses the univariate subexponential distributions, multivariate subexponential distributions and others. It also discusses the asymptotic behavior of the sums wherein it denotes probability distribution.