We investigate the power-dependent photoluminescence spectra from a strongly coupled quantum dot-cavity system using a quantum master equation technique that accounts for incoherent pumping, pure dephasing, and fermion or boson statistics. Analytical spectra at the one-photon correlation level and the numerically exact multi-photon spectra for fermions are presented. We compare to recent experiments on a quantum dot-micropiller cavity system and show that an excellent fit to the data can be obtained by varying only the incoherent pump rates in direct correspondence with the experiments. Our theory and experiments together show a clear and systematic way of studying stimulated-emission induced broadening and anharmonic cavity-QED. Introduction.-Single quantum dot (QD) -cavity systems facilitate the realization of solid state qubits (quantum bits) and have applications for producing single photons [1,2,3] and entangled photons [4,5]. Rich in physics and potential applications, the coupled QDcavity has been inspiring theoretical and experimental groups to probe deeper into the underlying physics of both weak and strong coupling regimes of semiconductor cavity-QED (quantum electrodynamics). Key signatures of cavity-QED include the Purcell effect and vacuum Rabi oscillations. Although a well known phenomenon in atomic cavity optics [6], vacuum Rabi splitting in a semiconductor cavity was only realized a few years ago [7,8,9]. Inspired by the recent surge of related experiments, many researchers have been working hard to develop new theoretical tools to understand the semiconductor cavity-QED systems. For example, the persistent excitation of the cavity mode for large excitoncavity detunings was measured [10,11], and qualitatively explained by extended theoretical approaches that account for coupling between the leaky cavity mode and the exciton, and by showing that the main contribution to the emitted spectrum comes from the cavity-mode emission [12,13,14,15,16]. These formalisms assume an initially excited exciton or an initially excited leaky cavity mode, and they are valid for low pump powers. However, an interesting question that has been posed recently, e.g., see Refs. [17,18,19], is what is the role of an incoherent pump on the photoluminescence (PL) spectra, where the pump can excite the exciton or cavity mode? To experimentally investigate the pump-dependent spectra, two recent experiments have been respectively reported by Münch et al. [20] for a QD-micropillar system, and by Laucht et al.[21] for a QD-photonic crystal system; these measurements show the pump-induced crossover from strong to weak coupling.In this work, we present a master equation (ME) the-