# One-Sided Multinomial Probabilities

Implements multinomial CDF (P(N1<=n1, ..., Nk<=nk)) and tail probabilities (P(N1>n1, ..., Nk>nk)), as well as probabilities with both constraints (P(l1.

`pmultinom` is a library for calculating multinomial probabilities. The probabilities that can be calculated include the multinomial cumulative distribution function: \$\$P(N_1 \le u_1, N_2 \le u_2, \cdots, N_k \le u_k)\$\$ In this case the usage would be

``````pmultinom(upper=us, size=n, probs=ps, method="exact")
``````

where `us` is the vector containing \$u_1, u_2, \cdots, u_k\$, and `n` and `ps` are the parameters of the multinomial distribution. This usage is analogous to the use of `pbinom`. Another important case is the probability of seeing more than some minimum number of observations in each category: \$\$P(N_1 > l_1, N_2 > l_2, \cdots, N_k > l_k)\$\$ In this case the usage would be

``````pmultinom(lower=ls, size=n, probs=ps, method="exact")
``````

where this time `ls` is the vector containing \$l_1, l_2, \cdots, l_k\$. Notice that in this case these are greater than signs, not greater than or equal signs. This is analogous to the usage of `pbinom` with `lower.tail=FALSE`. With some creativity, these can be adapted to calculate the probability that the maximum or minimum of a multinomial random vector is a given number, or that a given category will be the most or least observed. `pmultinom` also supports a more general usage, in which both lower and upper bounds are specified: \$\$P(l_1 < N_1 \le u_1, l_2 < N_2 \le u_2, \cdots, l_k < N_k \le u_k)\$\$ In this case the usage would be

``````pmultinom(lower=ls, upper=us, size=n, probs=ps, method="exact")
``````

See `vignette("pmultinom")` for the above text in Latex plus an example application. Many thanks to Aislyn Schalck for advice and encouragement.

# Reference manual

install.packages("pmultinom")

1.0.0 by Alexander Davis, 2 years ago

Browse source code at https://github.com/cran/pmultinom

Authors: Alexander Davis

Documentation:   PDF Manual

Task views: Probability Distributions