This paper studies the properties of the Cayley distributions, a new family of models for random pxp rotations. This class of distributions is related to the Cayley transform that maps a p(p-1)/2x1 vector s into SO(p), the space of pxp rotation matrices. First an expression for the uniform...

The asymptotic distribution of the Tukey median has recently been obtained by Nolan in a bivariate setting and by Bai and He in the general multivariate case. To establish their theorem, these authors made a strong symmetry hypothesis on the distribution and, in the case of Bai and He, assumed...

On the Banach space of real sequences converging to 0, it is shown that a probability measure may not possess an L1-median inside the space. This puts into better perspective previous results of existence of L1-medians obtained by Valadier and Kemperman.

For n [greater-or-equal, slanted] 2 an (n - 1)-parameter real process Vn, called stochastic volume, is defined. This process is an extension to higher dimensions of Lévy's stochastic area which is obtained from Vn by setting n = 2. For V3, a Strassen-type functional law of the iterated...

In applications it often occurs that the experimenter is faced with functions of random processes. Suppose, for instance, that he only can draw partial or incomplete information about the underlying process or that he has to classify events for the sake of efficiency. We assume that the...

It is shown that unimodality (discrete or not) is preserved by mixing for certain distributions. The technique of proof is essentially based on the Representation Theorem of Khinchin which characterizes unimodality.

Let F be a discrete distribution function on . This paper gives a characterization of discrete unimodal distribution functions (Theorem 5.1) and a representation theorem for those distribution functions (Theorem 6.3), both in terms of their Lévy concentration functions.