Effects of random deletion and additive noise on bunched and antibunched photon-counting statistics.

We examine the effect of Bernoulli random deletion and additive independent Poisson noise on photon-counting statistics. It is shown that under the action of such deletion and/or noise, both bunched and antibunched distributions move toward the Poisson distribution but never convert from bunched to antibunched or vice versa. Specific calculations are carried out for a number of examples of importance in optics.