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This paper is the first of a series devoted to theoretical studies of photon fluctuations in the light output of semiconductor injection lasers. Statistics on laser photon fluctuations are collected by means of a simulation of the dynamic behavior of the laser based on numerical solutions of noise driven laser rate equations. This first paper in the series introduces the noise driven rate equations for a single-cavity laser, explains the method used for their numerical solution, and discusses some approximate analytical results. The second paper presents results of photon counting statistics for the single-cavity laser collected from numerical solutions of the time dependent equations. Additional papers in this series will concentrate on coupled-cavity and distributed feedback lasers. Comparison of these statistical results will show clearly the advantage of coupled-cavity and distributed feedback laser designs over conventional single (Fabry-Perot) cavity injection lasers.