Our goal in this paper is to establish inequalities for the moments of decreasing variance residual life (DVRL) distributions. As a consequence we derive a new characterization of exponentiality. Then we use two of these inequalities to construct new tests for exponentiality versus DVRL....

We consider classes of discrete time Markov chains with continuous state space, the interval (0,1). These chains arise as stochastic models of phenomena in areas such as population theory, motion of particles in a random environment, etc. We exploit the Fréchet-Shohat theorem to establish that...

We present a direct, short and transparent proof of the following result: The product X1...Xn of independent exponential random variables X1,...,Xn is moment-indeterminate if and only if n=3. This and other complex analytic results concerning Stieltjes moment sequences and properties of the...

The aim of this paper is to exhibit an infinite family (Stieltjes class) of distributions all of which have the same moments as some powers of the inverse Gaussian distribution. For some particular cases of Stieltjes classes we have found the value of the index of dissimilarity.

Let F be a distribution function with all moments finite and such that the problem of moments for F has a nonunique solution (F is M-indeterminate). Our goal is to explicitly describe a Stieltjes class S= f[var epsilon]=f[1+[var epsilon]h],[var epsilon][set membership, variant][-1,1] of...

For any multivariate distribution with finite moments we can ask, as in the univariate case, whether or not the distribution is uniquely determined by its moments. In this paper, we summarize, unify and extend some results that are widely scattered in the mathematical and statistical literature....

For sets of random events or variables ranging from mutual independence to total dependence we introduce a dependency measure based on a more detailed definition of the independency property. The separating property of that measure allows to order sets of random elements as "more" or as "less"...