We present a theoretical model of a statistical ensemble, in which, unlike in conventional physics, the total number of particles and the energy are not fixed but bounded. It is shown that the temperature and the chemical potential play a dual role: they determine the average energy and the population of the levels in the system and at the same time they act as an imbalance between the energy and population ceilings and the corresponding average values. Different types of statistics (Boltzmann, Bose-Einstein, Fermi-Dirac and one corresponding to the description of a simple ecosystem) are considered. In all cases, we show that the systems may undergo a first or a second order phase transition akin to Bose-Einstein condensation for a non-interacting gas. We discuss numerical schemes for studying the new ensemble. The results of simulations are found to be in excellent agreement with theory.