The probability of the event of the multinomial distribution is given by the formula
(1) |
Two methods for this exist. One is based on Moran's inequality, which is not presented in its sharper version in textbooks like Feller [1957] or Johnson- Kotz-Balakrishnan [1997]. It is slow for large values of the number of the . By far more effective is the idea of Finucan [1964] to consider the step-function
(2) |
By a similar method the modes of a hypergeometric distribution can be calculated.
[1] | W. Feller [1968], An Introduction to Probability Theory and its Applications. J. Wiley 1950, 1957 and 1968. |
[2] | H.M. Finucan [1964], The mode of a Multinomial Distribution. Biometrica 51, 513-517. |
[3] | N.L. Johnson [1997], S. Kotz and N. Balkrishnan, Discrete Multivariate Distributions. J. Wiley 1997. |