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Multivariate Statistics Package Symbol

MultinomialDistribution

MultinomialDistribution[n, p]
represents a multinomial distribution with n trials and probability vector p.

To use MultinomialDistribution, 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 multinomial distribution is n!(p_i^x_i/x_i!).

The number of trials n can be any positive integer, and p can be any vector of non-negative real numbers that sum to unity.

MultinomialDistribution can be used with such functions as Mean, CDF and RandomInteger.

The mean of a multinomial distribution:

The variances of each dimension:

Probability density function:

Needs["MultivariateStatistics`"]

The mean of a multinomial distribution:

Needs["MultivariateStatistics`"]

The variances of each dimension:

Needs["MultivariateStatistics`"]

Probability density function:

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

The probability density function sums to unity:

A bivariate multinomial distribution is a binomial distribution:

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

MultinomialDistribution is not defined when the elements of p do not sum to 1:

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