This article descnbes a FORTRAN program that computes exact cumulative probabilities for the multinomial distribution. Two recursive routines eliminate the need for factorial expressions and provide for efficient calculation.
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References
1.
Dunlap, W. P. , Myers, L., & Silver, N. C. (1984). Exact multinomial probabilities for one-way contingency tables. Behavior Research Methods, Instruments, & Computers, 16, 54-56.