Wicksell's problem of unfolding ball size distributions is solved for the case of spherical spaces of curvature K > 0. The well-known formulas for the euclidean case result as limits if K → 0. The paper is completed by a brief discussion of some computer-aided statistical procedures.

An Ornstein-Uhlenbeck process subject to a quadratic killing rate is analyzed. The distribution for the process killing time is derived, generalizing the analogous result for Brownian motion. The derivation involves the use of Hermite polynomials in a spectral expansion.

Markov process are widely used to model computer systems. De Souza e Silva and Gail [3] calculated numerically the distribution of the cumulative operational time of repairable computer systems modelled by Markovian processes, that is, the distribution of the total time during which the system was in operation over a finite observation period. An extension of their approach is presented here. A closed-form solution is obtained for the distribution of the total time spent in a subset of states of a homogeneous Markov process during a finite observation period, which is theoretically and numerically interesting. We also give an application of this result to a fault-tolerant system.

We consider several classical notions of partial orderings among life distributions which have been used to describe ageing properties and tail domination. We show that if a distribution G dominates another distribution F in one of these partial orderings introduced here, and if two moments of G agree with those of F, including the moment that describes this partial ordering, then G = F. This leads to a characterization of the exponential distribution among HNBUE and HNWUE life distribution classes, and thus extends the results of Basu and Bhattacharjee (1984) and rectifies an error in that paper.

A characterization of the exponential distribution was obtained by Grosswald et al. (1980) using the relevation transform introduced by Krakowski (1973). Here we obtain an improved version of the result in Grosswald et al. (1980).

In an uncongested transportation network, adding routes and capacity to an existing network must decrease, or at worst not change, the average time individuals require to travel through the network from a source to a destination. Braess (1968) discovered that the same is not true in congested networks. Here we give an example of a queuing network in which added capacity leads to an increase in the mean transit time for everyone. Self-seeking individuals are unable to refrain from using the additional capacity, even though using it leads to deterioration in the mean transit time. This example appears to be the first queuing network to demonstrate the general principle that in non-co-operative games with smooth payoff functions, user-determined equilibria generically deviate from system-optimal equilibria.