Intelligent reflecting surface (IRS) has emerged as a promising technology to enhance the wireless communication network coverage and capacity by dynamically controlling the radio signal propagation environment. In contrast to the existing works that considered active or passive IRS only, we propose in this paper a new hybrid active-passive IRS architecture that consists of both active and passive reflecting elements, thus achieving their combined advantages flexibly. Under a practical channel setup with Rician fading where only the statistical channel state information (CSI) is available, we study the hybrid IRS design in a multi-user communication system. Specifically, we formulate an optimization problem to maximize the achievable ergodic capacity of the worst-case user by designing the hybrid IRS beamforming and active/passive elements allocation based on the statistical CSI, subject to various practical constraints on the active-element amplification factor and amplification power consumption, as well as the total active and passive elements deployment budget. To solve this challenging problem, we first approximate the ergodic capacity in a simpler form and then propose an efficient algorithm to solve the problem optimally. Moreover, we show that for the special case with all channels to be line-of-sight (LoS), only active elements need to be deployed when the total deployment budget is sufficiently small, while both active and passive elements should be deployed with a decreasing number ratio when the budget increases and exceeds a certain threshold. Finally, numerical results are presented which demonstrate the performance gains of the proposed hybrid IRS architecture and its optimal design over the conventional schemes with active/passive IRS only under various practical system setups.