Poisson approximation and dna sequence matching

The Poisson distribution is commonly used to model the number of occurrences of independent rare events. However, many instances arise where dependence exists, for example, in counting the length of long head runs in coin tossing, or matches between two DNA sequences. The Chen-Stein method of Poisson approximation yields bounds on the error incurred when approximating the number of occurrences of possibly dependent events by a Poisson random variable of the same mean. In addition to the problems related to the motivating examples from molecular biology involving runs and matches, the method may be applied to questions as varied as calculating probabilities involving extremes of sequences of random variables and approximating the probability of general birthday coincidences.