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. Author manuscript; available in PMC: 2013 Mar 2.
Published in final edited form as: Chem Phys. 2012 Mar 2;396:53–60. doi: 10.1016/j.chemphys.2011.06.006

Figure 2.

Figure 2

Comparison of various approximations for the probability Bij(N) of detecting N photons in the bins that undergo a single j → i transition. The exact (EX) distribution (dots, Eq. (10)) is compared with the negative binomial (NB) distribution (open circles, Eqs. (13) and (12)), the Gaussian (G) distribution (solid line, Eqs. (12) and (14)), the Poisson (PA) distribution with the average count rate (crosses, Eq. (15)), and the Poisson distribution (P) with the photon count rate of the initial state (triangles, Eq. (16)), which is implicit in the standard Hidden Markov Models. Mean numbers of photons in a bin in states i and j are (a) niT = 10, njT = 20; (b) niT = 10, njT = 50.