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High Quality Content by WIKIPEDIA articles! In probability and statistics the negative binomial distribution (including the Pascal distribution or Polya distribution) is a discrete probability distribution. It arises as the probability distribution of the number of failures in a sequence of Bernoulli trials needed to get a specified (non-random) number of successes. If one throws a die repeatedly until the third time a "1" appears, then the probability distribution of the number of non-"1"s that appear before the third "1" is a negative binomial distribution. The Pascal distribution and Polya distribution are special cases of the negative binomial. There is a convention among engineers, climatologists, and others to reserve "negative binomial" in a strict sense or "Pascal" (after Blaise Pascal) for the case of an integer-valued parameter r, to the right, and use "Polya" (for George Pólya) for the real-valued case. The Polya distribution more accurately models occurrences of "contagious" discrete events, like tornado outbreaks, than does the Poisson distribution.