The negative binomial distribution of order k is introduced and briefly studied. First it is shown that it is a proper probability distribution. Then its probability generating function, mean and variance are derived. Finally it is shown that the number of trials until the rth kth consecotive success ( r s 1, k L 1) in independent trials with constant success probability p ( 0 e p -z 1) is distributed as negative binomial distribution of order k. The K e y words: Negative linomial distribution of order k, generalized negative binomial distribution, probability generating function, mean, variance, waiting for the rtli kth consecutive success.
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