A photon counting estimates distribution of the average number of photons in coherent pulses

A statistical model linking the probability of detecting photons in a photon counting experiment to the average number of input photons is used to analytically derive an error distribution of the estimates of the average number of photons in coherent input pulses. The estimates distribution determines the required number of experimental count runs required for an acceptable measurement error, for any value of the average number of input photons. An expression for the minimum detectable power by photon counting is obtained, fully capturing the effect of the photon counting statistics thereby completing an earlier analysis.