Motivated by a real failure dataset in two-dimensional context, this paper presents an extension of the Markov modulated Poisson process (MMPP) to two dimensions. The one-dimensional MMPP has been proposed for modeling dependent and non-exponential inter-failure times (in contexts as queuing, risk or reliability, among others). novel allows dependence between sequences times, while at same time...

Uniqueness of specification of a bivariate distribution by a Pareto conditional and a consistent regression function is investigated. New characterizations of the Mardia bivariate Pareto distribution and the bivariate Pareto conditionals distribution are obtained.