egttools.distributions.multinomial_pmf

multinomial_pmf(x: Annotated[numpy.typing.NDArray[numpy.uint64], '[m, 1]'], n: SupportsInt | SupportsIndex, p: Annotated[numpy.typing.NDArray[numpy.float64], '[m, 1]']) → float

Calculate the probability mass function of a multinomial distribution.

This function returns the probability of drawing counts x in a sample of size n, given category probabilities p.

Parameters:

  • x (numpy.ndarray) – Counts for each category in the sample. Must sum to n.

  • n (int) – Total number of draws.

  • p (numpy.ndarray) – Category probabilities. Must sum to 1.

Returns:

Probability of observing the counts x.

Return type:

float

See also

egttools.distributions.multivariate_hypergeometric_pdf, egttools.distributions.binom, egttools.distributions.comb

Examples

>>> import numpy as np
>>> from egttools.numerical.distributions import multinomial_pmf
>>> multinomial_pmf(np.array([2, 1]), 3, np.array([0.5, 0.5]))