NegativeMultinomialDistribution[n, p]
represents a negative multinomial distribution with parameter n and failure probability vector p.


  • The probability for a vector of non-negative integers , , ..., , where is the length of in a negative multinomial distribution, is proportional to .
  • The parameter n can be any positive real number, and p can be any vector of non-negative real numbers that sum to less than unity.
  • If n is a positive integer, NegativeMultinomialDistribution[n, p] gives the distribution of the failure counts in a sequence of trials with success probability 1-Total[p] and Length[p] types of failure before n successes occur.
  • NegativeMultinomialDistribution can be used with such functions as Mean, CDF, and RandomVariate.
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