Suppose that P{Xn = i} = p(1p)i1, i 1. That is, suppose that the interarrival distribution is
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Suppose that P{Xn = i} = p(1−p)i−1, i 1. That is, suppose that the interarrival distribution is geometric. Now S1 = X1 may be interpreted as the number of trials necessary to get a single success when each trial is independent and has a probability p of being a success. Similarly, Sn may be interpreted as the number of trials necessary to attain n successes, and hence has the negative binomial distribution
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