A new multivariate distribution possessing arbitrarily parametrized and positively dependent univariate Pareto margins is introduced. Unlike the probability law of Asimit et al. (2010), the structure in this paper is absolutely continuous with respect to the corresponding Lebesgue measure. The distribution is of importance to actuaries through its connections to the popular frailty models, as well as because of the capacity to describe dependent heavy-tailed risks. The genesis of the new distribution is linked to a number of existing probability models, and useful characteristic results are proved. Expressions for, e.g., the decumulative distribution and probability density functions, (joint) moments and regressions are developed. The distributions of minima and maxima, as well as, some weighted risk measures are employed to exemplify possible applications of the distribution in insurance.

Piezoelectric materials have a strong interaction between their mechanical and electrical properties that translates into innovative components and circuits architectures. This work describes an original method using the electromechanical properties of the aluminum nitride (AlN) piezoelectric material to characterize its vertical extension when an electric field is applied. The novel techniques based on measurements of a planar parallel plate AlN capacitor without and with bias employing an impedance analyzer. The parallel plate capacitor theory and piezoelectric material analysis are used to calculate the vertical displacement of the AlN film.

We examine how the binomial distribution B(n,p) arises as the distribution Sn = ∑i=1nXi of an arbitrary sequence of Bernoulli variables. It is shown that B(n,p) arises in infinitely many ways as the distribution of dependent and non-identical Bernoulli variables, and arises uniquely as that of independent Bernoulli variables. A number of illustrative examples are given. The cases B(2,p) and B(3,p) are completely analyzed to bring out some of the intrinsic properties of the binomial distribution. The conditions under which Sn follows B(n,p), given that Sn-1 is not necessarily a binomial variable, are investigated. Several natural characterizations of B(n,p), including one which relates the binomial distributions and the Poisson process, are also given. These results and characterizations lead to a better understanding of the nature of the binomial distribution and enhance the utility.

The classical martingale characterizations of the Poisson process were obtained for point process or purely discontinuous martingale i.e. under additional assumptions on properties of trajectories. Here our aim is to search for related characterizations without relying on properties of trajectories. Except for a new martingale characterization, results based on conditional moments jointly involving the past and the nearest future are presented.

A stability theorem determines the extent to which the conclusions of a given theorem are affected if the assumptions of the theorem are not exactly but only approximately satisfied. The meaning of the word ‘approximately’ has to be defined exactly. The stability of decomposition theorems, of characterizations by independence and by regression properties are the primary object of the paper.

Yu. V. Linnik showed that certain transformations, given by Formulae (1.1), (1.6) and (1.7) transform a normal sample into itself. The transformations (1.1) and (1.7) apply to samples of size 2 while (1.6) admits an arbitrary sample size. It is also assumed that the population mean is zero.

In the present paper the converse theorems are proven so that characterizations of the normal distribution are obtained. The problem leads to the functional equations (2.3) and (2.13) whose solution yields the desired results.