MultivariateStatistics`

NegativeMultinomialDistribution

As of Version 8, NegativeMultinomialDistribution is part of the built-in Wolfram Language kernel.

NegativeMultinomialDistribution[n,p]

represents a negative multinomial distribution with parameter n and failure probability vector p.

Details and Options

To use NegativeMultinomialDistribution, you first need to load the Multivariate Statistics Package using Needs["MultivariateStatistics`"].
The probability for a vector x of non-negative integers x₁, x₂, …, x_Length[p] in a negative multinomial distribution is proportional to (n-1+∑x_i)!∏(p_i^x_i/x_i!).
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 RandomInteger.

open allclose all

The mean of a negative multinomial distribution:

The variances of each dimension:

Probability density function:

Generate a set of pseudorandom vectors that follow a negative multinomial distribution:

A univariate negative multinomial distribution is a negative binomial distribution:

NegativeMultinomialDistribution is not defined when n is not a positive integer:

NegativeMultinomialDistribution is not defined when p is not a vector of probabilities that sums to less than 1:

Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:

Top