A general solution of the Deny convolution equation restricted to a half line is obtained using certain concepts of random walk theory. The equation in question arises in several places in applied probability such as in queueing and storage theories and characterization problems of probability...

We establish certain general characterization results on elliptically symmetric distributions and exchangeable random variables. These results yield, in particular, the results given earlier by Maxwell, Bartlett, Kingman, Ali, Smith, Arnold and Lynch, and several others.

Inequalities and monotonicity results are obtained for order statistics from distributions ordered by dispersivity. One results solves the open problem posed by Marshall and Olkin (1979, p. 282). Applications of these results are given.

In this paper, a new family of distributions is introduced which we name the generalized Euler distributions. This family arises as a consequence of investigating optimal strategies for drilling in an oil exploration model. Properties of this family are presented.