pmultinom

The multinomial cumulative distribution function is weirdly absent from the R core libraries. This package fills that gap. It's implemented in C++ for efficiency and uses syntax you're probably familiar with.

Installation

pmultinom depends on the GNU scientific library (GSL), if you have trouble with the installation, double check that it's installed and set up correctly on your system.

Debian (Ubuntu/Linux Mint)

  sudo apt-get install gsl-bin libgsl0-dev

Then from within R:

  install.packages('devtools')
  devtools::install_github('fennerm/pmultinom')

MacOS

   brew install gsl

Then from within R:

   install.packages('devtools')
   devtools::install_github('fennerm/pmultinom')

Other GNU/Linux

Download the gsl development library for your distro, then install with devtools as above.

Usage

pmultinom exports a single function:

    pmultinom(q, n, prob, log.p = FALSE, lower.tail = TRUE)

Arguments

       q: Vector of quantiles; If q has length 1 then the same quantile
          is used for each bin. If q is length k, each bin is assigned
          its own quantile

       n: Total number of balls

    prob: A vector of length k, describing the probability of a ball
          being placed into bin xk

    log.p: If TRUE, natural logarithm of probability is returned
           (Default: FALSE)

    lower.tail: logical; if TRUE, probabilities are P[X <= x],
          otherwise, P[X > x] (Default: TRUE)

Examples

For 4 balls randomly thrown into 2 bins, probability that all bins end up with 2 or fewer balls

pmultinom(q = 2, n = 4, prob = c(0.5, 0.5))
[1] 0.3361880568`

For 6 balls randomly thrown into 3 bins, probability that at least one bin ends up with 3 or more balls

pmultinom(q = 2, n = 6, c(1/3, 1/3, 1/3), lower.tail = FALSE)
[1] 0.8857285167

Same as above, but with different probabilities for each bin

pmultinom(q = 2, n = 6, c(0.2, 0.3, 0.5), lower.tail = FALSE)
[1] 0.9250331024

Credit

• Glenn Stone (staff.scm.uws.edu.au/~glenn) for the original C implementation.