Tests for the parameters of a Multinomial distribution

Tests for the parameters of a multinomial distribution and their properties and assumptions.

Test Purpose
Pearson X² Tests if the proportions are equal to the hypothesized values.

Uses the score statistic and computes an asymptotic p-value.

Likelihood ratio G² Tests if the proportions are equal to the hypothesized values.

Uses the likelihood ratio statistic and computes an asymptotic p-value.

Pearson X² usually converges to the chi-squared distribution more quickly than G². The likelihood ratio test is commonly used in statistical modeling as the G² statistic is easier to compare between different models.