In this paper, we summarize the photon emission statistical properties of
single molecule system, using the recently developed generating function method.
Through the introduce of one or double “auxiliary” variables, we can investigate the
first moment and second moment of photon emission statistics driven by different
external fields, such as the line shapes and Mandel's Q parameters, the photon emission
probabilities, the probability distribution of time between successive emission, the
waiting time and the waiting time distribution, the cross correlation, the joint probabilities,
etc. Among,the first moment of photon statistics and the experimental results
of optical amplification are in good agreement.