and a family of the multinomial distributions is defined by . Then the equivalence test problem is given by and . The distance is usually computed using numerical optimization. The tests for this case are developed recently in Ostrovski (2018). Random variate generation First, reorder the parameters such that they are sorted in descending order (this is only to speed up computation and not strictly necessary). Now, for each trial, draw an auxiliary variable X from a uniform (0, 1) distribution. The resulting outcome is the component {Xj = 1, Xk = 0 for k ≠ j } is one observation from the multinomial distribution with and n = 1. A sum of independent repetitions of this experiment is an observation from a multinomial distribution with n equal to the number of such repetitions. References Citations Sources Discrete distributions Multivariate discrete distributions Factorial and binomial topics Exponential family distributions